Month: July, 2016

Hans Freudenthal (1905-1990). This photograph is assumed to be copyrighted and unlicensed, but qualifies as fair use under United States copyright law to illustrate the subject in question where no free equivalent is available, as Professor Freudenthal is deceased and no free replacement can be made.

“Almost at the bounds of science fiction, though still with an undoubted scientific interest, is the project of the Dutch mathematician Hans A. Freudenthal (Lincos, 1960) for a language in which eventual encounters with the inhabitants of other galaxies may be conducted (see Bassi 1992).

Lincos is not designed as a language to be spoken; it is rather a model for inventing a language and at the same time teaching it to alien beings that have presumably traditions and biological structure different from ours.

Freudenthal starts off by supposing that we can beam into space signals, which we might picture as radio waves of varying length and duration. The significance of these waves derives not from their expression-substance, but rather from their expression-form and content-form.

By endeavoring to understand the logic that determines the expression-form being transmitted to them, the space aliens are supposed to extrapolate a content-form that will not be alien to them.

During the first phase, the messages consist of regular sequences of pulses. These are intended to be interpreted quantitatively–four pulses standing for the number 4, etc. As soon as it is assumed that the aliens have correctly interpreted these first signals, the transmission passes to the second phase, in which it introduces simple arithmetic operators:

* * * < * * * *

* * * * = * * * *

* * * * + * * = * * * * * *

In the next phase, the aliens are taught to substitute for the pulses a system of binary numbers (in which * * * * = 100, * * * * * = 101, * * * * * * = 110); this makes it possible, using only ostension and repetition, to communicate some of the principle operations in mathematics.

The transmission of temporal concepts presents a more complex problem. Freudenthal, however, presumes that by constantly receiving a signal of the same duration, constantly associated to the same number of pulses, the aliens will begin to compute a certain duration in seconds. Lincos also teaches conversational rules, training the aliens to understand sequences such as “Ha says to Hb: what is that x such that 2x = 5?”

In one sense, we are treating the space aliens like circus animals; we subject them to a repeated stimulus, giving them positive reinforcement whenever they exhibit the desired response. In the case of animals, however, the reinforcement is immediate–we give them food; in the case of aliens, the reinforcement cannot but be a broadcast signal that they should interpret as “OK.”

By this means, the aliens are meant to learn to recognize not only mathematical operations but also concepts such as “because,” “as,” “if,” “to know,” “to want,” and even “to play.”

The project presupposes that the alines have the technological capability to receive and decode wave-length signals, and that they follow logical and mathematical criteria akin to our own.

They should share with us not only the elementary principles of identity and non-contradiction, but also the habit of inferring a constant rule through induction from many similar cases.

Lincos can only be taught to those who, having guessed that for the mysterious sender 2 x 2 = 4, will assume that this rule will remain constant in the future. This is, in fact, a big assumption; there is no way of ruling out that there exist alien cultures who “think” according to rules which vary according to time and circumstances.

What Freudenthal is aiming for is, explicitly, a true characteristica universalis; in Lincos, however, only a handful of original syntactic rules are formulated in the beginning. As to the rest (as to, for example, the rules governing questions and answers), the model implicitly assumes that the interlocutors will use the rules, and even the pragmatics, of a natural language.

We can, for example, imagine a community of angels, each of whom either reads the thoughts of the others or learns truths directly through beholding them in the mind of God: for such beings, the set of interactional rules governing questions and answers would make no sense at all.

The problem with Lincos is that, although provided with a formal structure, it is conceived as an instrument for “natural” communication, and thus it is inherently uncertain and imprecise. In other words, it cannot possess the tautological structure of a formalized language.

Lincos is probably more interesting from a pedagogical point of view: can one teach a language without ostension?

If the answer is positive, Lincos would allow a situation different from that imagined by philosophers of language, when they skeptically imagine a scene in which a European explorer interacts with a native, each party tries to communicate with the other by pointing at bits of space-time and uttering a given sound, and there is no way for the explorer to be certain whether the native is denoting a given object located in that space-time portion, or the fact that something is happening there, or is expressing his or her refusal to answer (see Quine 1960).”

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Giovanni Giuseppe Matraja, Genigrafia italiana, 1831. Original held at the University of Illinois at Urbana-Champaign, with a glorious eBook format posted by the Hathitrust and GoogleBooks among others. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“Vismes was not the only one to fall foul of this seemingly elementary snare. In 1831 Father Giovan Giuseppe Matraja published his Genigrafia italiana, which is nothing other than a polygraphy with five (Italian) dictionaries, one for nouns, one for verbs, one for adjectives, one for interjections and one for adverbs.

Since the five dictionaries account for only 15,000 terms, Matraja adds another dictionary that lists 6,000 synonyms. His method managed to be both haphazard and laborious: Matraja divided his terms into a series of numbered classes each containing 26 terms, each marked by an alphabetical letter: thus A1 means “hatchet,” A2 means “hermit,” A1000 means “encrustation,” A360 means “sand-digger,” etc.

Even though he had served as a missionary in South America, Matraja was still convinced that all cultures used the same system of notions. He believed that western languages (all of which he seemed to imagine were derived from Latin grammar) might perfectly well serve as the basis for another language, because, by a special natural gift, all peoples used the same syntactic structures when speaking–especially American Indians.

In fact, he included a genigraphical translation of the Lord’s Prayer comparing it with versions in twelve other languages including Nahuatl, Chilean and Quechua.

In 1827 François Soudre invented the Solresol (Langue musicale universelle, 1866). Soudre was also persuaded that the seven notes of the musical scale composed an alphabet comprehensible by all the peoples of the world, because the notes are written in the same way in all languages, and could be sung, recorded on staves, represented with special stenographic signs, figured in Arabic numerals, shown with the seven colors of the spectrum, and even indicated by the touch of the fingers of the right and left hands–thus making their representation comprehensible even for the deaf, dumb and blind.

It was not necessary that these notes be based on a logical classification of ideas. A single note expresses terms such as “yes” (musical si, or B) and “no” (do, or C); two notes express pronouns (“mine” = redo, “yours” = remi); three notes express everyday words like “time” (doredo) or “day” (doremi).

The initial notes refer to an encyclopedic class. Yet Soudre also wished to express opposites by musical inversion (a nice anticipation of a twelve-tone music procedure): thus, if the idea of “God” was naturally expressed by the major chord built upon the tonic, domisol, the idea of “Satan” would have to be the inversion, solmido.

Of course, this practice makes nonsense of the rule that the first letter in a three-note term refers to an encyclopedic class: the initial do refers to the physical and moral qualities, but the initial sol refers back to arts and sciences (and to associate them with Satan would be an excess of bigotry).

Besides the obvious difficulties inherent in any a priori language, the musical language of Soudre added the additional hurdle of requiring a good ear. We seem in some way to be returning to the seventeenth century myth of the language of birds, this time with less glossolalic grace, however, and a good deal more pure classificatory pedantry.

Couturat and Leau (1903: 37) awarded to the Solresol the encomium of being “the most artificial and most impracticable of all the a priori languages.” Even its number system is inaccessible; it is based on a hexadecimal system which, despite its claims to universality, still manages to indulge in the French quirk of eliminating names for 70 and 90.

Yet Soudre labored for forty-five years to perfect his system, obtaining in the meantime testimonials from the Institut de France, from musicians such as Cherubini, from Victor Hugo, Lamartine and Alexander von Humboldt; he was received by Napoleon III; he was awarded 10,000 francs at the Exposition Universale in Paris in 1855 and the gold medal at the London Exposition of 1862.

We will content ourselves with a brief account of the Projet d’une langue universelle of Sotos Ochando (1855). Its theoretical foundations are comparatively well reasoned and motivated; its logical structure could not be of a greater simplicity and regularity; the project proposes–as usual–to establish a perfect correspondence between the order of things signified and the alphabetical order of the words that express them.

Unfortunately–here we go again–the arrangement is empirical: A refers to inorganic material things, B to the liberal arts, C to the mechanical arts, D to political society, E to living bodies, and so forth.

With the addition of the morphological rules, one generates, to use the mineral kingdom as an example, the words Ababa for oxygen, Ababe for hydrogen, Ababi for nitrogen, Ababo for sulphur.

If we consider that the numbers from one to ten are siba, sibe, sibi, sibo, sibu, sibra, sibre, sibri, sibro, and sibru (pity the poor school children having to memorize their multiplication tables), it is evident that words with analogous meanings are all going to sound the same.

This makes the discrimination of concepts almost impossible, even if the formation of names follows a criterion similar to that of chemistry, and the letters stand for the components of the concept.

The author may claim that, using his system, anyone can learn over six million words in less than an hour; yet as Couturat and Leau remark (1903: 69), learning a system that can generate six million words in an hour is not the same as memorizing, recognizing, six million meanings.

The list could be continued, yet towards the end of the nineteenth century, news of the invention of a priori languages was becoming less a matter for scientific communications and more one for reports on eccentric fellows–from Les fous littéraires by Brunet in 1880 to Les fous littéraires by Blavier in 1982.

By now, the invention of a priori languages, other than being the special province of visionaries of all lands, had become a game (see Bausani 1970 and his language Markuska) or a literary exercise (see Yaguello 1984 and Giovannoli 1990 for the imaginary languages of science fiction).

In 1774, the Italian-Swiss Father Francesco Soave published his Riflessioni intorno alla costituzione di una lingua universale. Soave, who had done much to spread the sensationalist doctrine to Italy, advanced a criticism of the a priori languages that anticipated those made by the Idéologues (on Soave see Gensini 1984; Nicoletti 1989; Pellerey 1992a).

Displaying a solid understanding of the projects from Descartes to Wilkins and from Kircher to Leibniz, on the one hand Soave advanced the traditional reservation that it was impossible to elaborate a set of characters sufficient to represent all fundamental concepts; on the other hand, he remarked that Kalmar, having reduced these concepts to 400, was obliged to give different meanings to the same character, according to the context.

Either one follows the Chinese model, without succeeding in limiting the characters, or one is unable to avoid equivocations.

Unfortunately, Soave did not resist the temptation of designing a project of his own, though outlining only its basic principles. His system of classification seems to have been based on Wilkins; as usual he sought to rationalize and simplify his grammar; at the same time, he sought to augment its expressive potential by adding marks for new morphological categories such as dual and the neuter.

Soave took more care over his grammar than over his lexicon, but was mainly interested in the literary use of language: from this derives his radical skepticism about any universal language; what form of literary commerce, he wondered, could we possibly have with the Tartars, the Abyssinians or the Hurons?

In the early years of the next century, Soave’s discussion influenced the thinking of Giacomo Leopardi, who had become an exceptionally astute student of the Idéologues.

In his Zibaldone, Leopardi treated the question of universal languages at some length, as well as discussing the debate between rationalists and sensationalists in recent French philosophy (see Gensini 1984; Pellerey 1992a).

Leopardi was clearly irritated by the algebraic signs that abounded in the a priori languages, all of which he considered as incapable of expressing the subtle connotations of natural languages:

“A strictly universal language, whatever it may be, will certainly, by necessity and by its natural bent, be both the most enslaved, impoverished, timid, monotonous, uniform, arid, and ugly language ever.

It will be incapable of beauty of any type, totally uncongenial to imagination [ . . . ] the most inanimate, bloodless, and dead whatsoever, a mere skeleton, a ghost of a language [ . . . ] it would lack life even if it were written by all and universally understood; indeed it will be deader than the deadest languages which are no longer either spoken or written.” (23 August 1823, in G. Leopardi, Tutte le opere, Sansoni: Florence 1969: II, 814).

Despite these and similar strictures, the ardor of the apostles of philosophic a priori languages was still far from quenched.

Vismes argued that when the Latin translation of Genesis 11:1-2 states that “erat terra labii unius” (a passage to which we usually give the sense that “all the world was of one language”), it used the word labium (lip) rather than lingua (tongue) because people first communicated with each other by emitting sounds through their lips without articulating them with their tongue.

Music was not a human invention (pp. 1-20), and this is demonstrated by the fact that animals can understand music more easily than verbal speech: horses are naturally roused by the sound of trumpets as dogs are by whistles. What is more, when presented with a musical score, people of different nations all play it the same way.

Vismes presents enharmonic scales of 21 notes, one for each letter of the alphabet. He did this by ignoring the modern convention of equal temperament, and treating the sharp of one note as distinct from the flat of the note above.

Since Vismes was designing a polygraphy rather than a spoken language, it was enough that the distinctions might be exactly represented on a musical stave.

Inspired, perhaps, indirectly by Mersenne, Vismes went on to demonstrate that if one were to combine his 21 sounds into doublets, triplets, quadruplets, etc., one would quickly arrive at more syntagms than are contained in any natural language, and that “if it were necessary to write down all the combinations that can be generated by the seven enharmonic scales, combined with each other, it would take almost all of eternity before one could hope to come to an end.” (p. 78).

As for the concrete possibility of replacing verbal sounds by musical notes, Vismes devotes only the last six pages of his book to such a topic–not a great deal.

It never seems to have crossed Visme’s mind that, in taking a French text and substituting tones for its letters, all he was doing was transcribing a French text, without making it comprehensible to speakers of other languages.

Vismes seems to conceive of a universe that speaks exclusively in French, so much so that he even notes that he will exclude letters like K, Z and X because “they are hardly ever used in languages” (p. 106).”

“Even though the primitives were no longer such, they remained a compositional criterion. For instance, given in first position the letter a, which refers to grammar, the depending letters have a mere distinctive value and refer back to grammatical sub-categories.

A third and final letter specifies a morphological termination or other derivation. Thus a list of terms is derived: ava (grammar), ave (letter), alve (vowel), adve (consonant) and so on. The expressions function like a chemical formula, which synthetically reveals the internal composition of its content, and like a mathematical expression in that the system attributes to each letter a value determined by its position.

Nevertheless, this theoretical perspicuity is bought at a dear price because, in practice, the lexicon becomes obsessively monotonous.

Equally, the Pasigraphie of De Maimieux institutes a graphic code of twelve characters that can be combined according to fixed rules. Each combination expresses a definite thought (the model is the Chinese character).

Other characters are placed on the outside of the “body” of the word to modify the central idea. The body of the word can contain three, four or five characters. Words of only three characters signify either “pathetic” terms or connectives linking parts of discourse, and are classified in an indicule.

Words of four characters stand for ideas in practical life (like friendship, kinship, business), and are classified in petit nomenclateur. Five character words concern categories such as art, religion, morality, science and politics, and are classified in a grand nomenclateur.

None of these categories is primitive; they have rather been isolated in terms of common sense as the most manageable way of subdividing contemporary knowledge. De Maimieux went so far as to admit that he had not sought for an absolute ordering but rather any ordering whatsoever, fût-il mauvais (p. 21).

The system, unfortunately, provides no way of eliminating synonyms; they are constitutional, and De Maimieux only says how to identify them. In fact, every expression in the pasigraphy can be connected not to a single meaning but to three or four different contents.

These different meanings can be distinguished according to the position of the characters on a sort of pentagram. This method imposes no small amount of tedium on the reader, who, as the characters display no iconic similarity with their content, is continually forced to consult the indicule, the petit nomenclateur or the grand nomenclateur, depending on the length of the expression.

Thus, to give an example, if we run across a five letter syntagm, we must seek first in the grand nomenclateur

“the class that begins with the first character of the term. Inside this class, we seek for the framework listing the second character of the term. Inside this framework, we seek for the column containing the third character of the term. Finding the right column, we seek the section (tranche) with the fourth character of the term.

Finally, within this section we seek the line containing the fifth character. At this point we will discover that, as the meaning, we have found a line listing four verbal words; it will then be necessary to observe which of the characters in the pasigraphic term is graphically tallest in order to determine which of the four possible words is the one corresponding to the term.” (Pellerey 1992a: 104).

A real piece of drudgery, though not enough to dampen the ardor of the project’s enthusiasts, who, starting with the abbé Sicard and finishing with various contemporary reviewers wishing to favor the diffusion of the system, entered into pasigraphic correspondence with each other and with De Maimieux, who even composed pasigraphic poetry.

De Maimieux spoke of his pasigraphy as an instrument for checking the accuracy of translations. Many theories of translation, in fact, presuppose the existence of a “parameter language” with which one can control the correct correspondence between the original text and the translated one.

De Maimieux aimed at proposing a supposedly neutral metalanguage which could track the correspondence between expressions in System A and those in system B. What was never placed in discussion was the fact that the content of this metalanguage was structured along the lines of Indo-European languages, and of French in particular.

As a consequence we have “the immense drama of ideography: it can identify and describe its contents, which are supposedly ideas or notions in themselves, only by naming them with words from a natural language–a supreme contradiction for a project created expressly to eliminate verbal languages.” (Pellerey 1992a: 114).

As can be seen, neither in technique nor in underlying ideology have we advanced very far from the time of Wilkins.

(Editorial note: Eco writes “De Ria,” yet Google returns “Jean-Pierre Deriaz” as the author of the work, and beautifully offers the 1787 document as a free eBook. Thank you, Google. Yet, history must agree with Eco, as the title page depicts the author as “J.P. De Ria,” as Eco attests.).

Despite its pretentious title, the book is nothing but a manual of phonetics or, perhaps, a proposal for the orthographic reform of French, written in a febrile, quasi-mystic style.

It is not in the least clear how the reform could be applied to all the languages of the world (it would, for example, be particularly inapplicable to English phonetics); but this is an unimaginable question for the author.

Returning to De Maimieux, the flexibility displayed in his choice of the pseudo-primitives seems to associate his project with the empiricist tendencies of the Encyclopédie; yet, once they were chose, his belief in them, and the self-confidence with which he sought to impose them on everyone else, still reflected the rationalist temperament.

In this respect, it is interesting to note that De Maimieux sought to provide for the rhetorical use of his language and the possibility of oratory: we are, of course, in a time of eloquence where the life or death of a revolutionary faction might depend on its ability to sway its audience by the force of its words.

Where the a priori linguists of the eighteenth-century were most critical of their predecessors, however, was in the matter of grammar. All were inspired by the “laconic” ideal proposed in the Encyclopédie.

In the grammar of De Maimieux, the number of grammatical categories originally projected by Faiguet is somewhat amplified; in the case of Delormel, however, the grammar is so laconic that Couturat and Leau (1903: 312), who spend long chapters describing other systems, liquidate his in a page and a half (Pellerey’s treatment is more accurate and generous; 1992a: 125).

Hourwitz, whose project remains akin to the seventeenth century polygraphies, produced a grammar that was, perhaps, the most laconic of all: one declension, one conjugation for verbs; the verbs were to be expressed in the infinitive with a few additional signs that specify tense and mood.

The tenses themselves were reduced to a system of three steps from the present, either backwards or forwards in time: thus A 1200 means “I dance;” A/1200 means “I have danced;” A 1200/ means “I will dance.”

What was the need for a universal language, asked the count, when a perfect language existed already? The language was, of course, French. Apart from its intrinsic perfection, French was already an international language; it was the language most diffused in the world, so much that it was possible to speak of the “French world” just as, in antiquity, one could speak of the “Roman world.” (p. 1).

According to de Rivarol, French possessed a phonetic system that guaranteed sweetness and harmony, as well as a literature incomparable in its richness and grandeur; it was spoken in that capital city which had become the “foyer des étincelles répandues chez tous les peuples” (p. 21).

In comparison with French all other languages paled: German was too guttural, Italian too soft, Spanish too redundant, English too obscure. Rivarol attributed the superiority of French to its word order: first subject, then verb, and last object. This word order mirrored a natural logic which was in accordance with the requirements of common sense.

This common sense is, however, linked to the higher activity of our minds: for if we were to base our syntactical order on the order of our perceptions, it is plain that we would start with the object, which first strikes our senses.

The polemical reference to the sensationalism of Condillac is evident when de Rivarol asserts that, if other people, speaking in other tongues, had abandoned the natural, direct word order, it was because they had let their passions prevail over their intellect (p. 25-6).

This retreat from natural reason, moreover, was responsible for the syntactic inversion that had provoked the confusions and ambiguities prevalent in natural languages other than French. Naturally, those languages which tried to compensate for their lack of direct word order with declensions were among the most confused of all.

We might bear in mind that, even though, in 1784, while he was writing his pamphlet, de Rivarol was an habitué of Enlightenment circles, after the advent of the revolution, he revealed himself to be a conservative legitimist.

To a man so spiritually tied to the ancien régime, the philosophy and linguistics of the sensationalists may (quite justifiably) have appeared as a harbinger of an intellectual revolution which emphasized the passions as the fundamental force motivating humanity.

If this were the case, then “the direct word order acquires the value of an instrument of protection [ . . . ] against the inflammatory style of the public orators who, in a few short years, would be preaching revolution and manipulating the masses.” (Pellerey 1992a: 147).

Yet what really characterized the eighteenth century debate was the desire not so much to simplify grammar as to show that there existed a natural and normal grammar, universally present in all human languages. This grammar is not, however, manifestly apparent; it must be sought instead beneath the surface of human languages, all of which are, in some degree or other, derivations from it.

As can be seen, we have returned to the ideal of a universal grammar, only now one is trying to identify it by reducing every existing language to its most laconic form.

Attentive as we have been throughout this story to the issue of side-effects, we ought here to note that without this eighteenth century intuition of an original, laconic grammar, our contemporary notions of generative and transformational grammar would be quite inconceivable, even if their origins are usually traced back to the Cartesianism of Port Royal.”

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François Fénelon (1651-1715), Telemachus, or the first page of the first book of Les Aventures de Télémaque, first published anonymously in 1699, and translated into English in London in 1715. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

As the title itself suggests, the project was for a polygraphy, in the sense we saw in Kircher, and, at most, it is worthy of note in that its attempt to include a contracted grammar points the way to future developments.

In any case, the proposal is distinguished by including an appeal, by the anonymous author, for a commission which would develop the project and for a prince who would impose its adoption.

Such an appeal “cannot help but remind us of a possibility, which must have seemed evident in the year 1720, that a phase of stability for Europe was about to open, and that, consequently, sovereigns might be expected to be more willing to patronize linguistic and intellectual experiments” (cf. Pellerey 1992a: 11).

In his article on “Langue” in the Encyclopédie, even a rationalist like Beauzée had to concede that, since it would be difficult to come to an agreement over a new language, and an international language still seemed to him to be necessary, Latin had to remain the most reasonable candidate.

For their part, the empiricists among the encyclopedists felt duty-bound to consider the idea of a universal language, too. As a sort of coda to the article on “Langue,” Joachim Faiguet wrote four pages on a project for a langue nouvelle. Couturat and Leau (1903: 237) consider this as representing a first attempt at overcoming the problems inherent in the a priori languages and at sketching out an example of the a posteriori languages we will be discussing in the next chapter.

As his model, Faiguet took a natural language–French. He formed his lexicon on French roots, and concentrated on the delineation of a simplified and regularized grammar, or a “laconic” grammar.

Following the authors in the previous century, Faiguet eliminated those grammatical categories that seemed to him redundant: he suppressed the articles, substituted flexions with prepositions (bi for the genitive, bu for the dative, and de and po for the ablative), transformed adjectives (indeclinable) into adverbial forms, standardized all plurals (always expressed by an s); he simplified verb conjugations, making them invariable in number and person, adding endings that designated tenses and modes (I give, you give, he gives became Jo dona, To dona, Lo dona); the subjunctive was formed by adding an r to the stem, the passive by the indicative plus sas (meaning to be: thus to be given became sas dona).

Faiguet’s language appears as wholly regular and without exceptions; every letter or syllable used as endings had a precise and unique grammatical significance. Still, it is parasitic on French in a double sense: not only is it a “laconicized” French at the expression-level; it is French that supplies the content-level as well. Thus Faiguet’s was little less than a sort of easy-to-manage Morse code (Bernadelli 1992).

As can be seen, De Maimieux’s project was a pasigraphy–that is, a universal written language. Since, however, in 1799 this same author had also formulated a pasilalie–adding rules for pronouncing his language–his project can be considered as an a priori language.

For its part, Hourwitz’s project was for a polygraphy, too–even though he seemed unaware that his was by no means the first project of this type. Still, in its structure, Hourwitz’s polygraphy was an a priori language.

Although all three projects still followed the principles laid down in the seventeenth century tradition, they were different in three fundamental ways: their purposes, the identification of their primitives, and their grammars.

De Maimieux spoke of communication between European nations, between Europeans and Africans, of providing a means of checking the accuracy of translations, of speeding up diplomacy and civil and military undertakings, of a new source of income for teachers, writers and publishers who should “pasigraphize” books written in other languages.

Hourwitz added to this list other purely practical considerations, such as the advantages in the relations between doctors and patients or in courtroom procedures. As one symptom of a new political and cultural atmosphere, instead of using the Lord’s Prayer as a sample translation, Hourwitz chose the opening of Fénelon’sAventures de Télemaque–a work which, despite its moralizing bent, was still a piece of secular literature portraying pagan gods and heroes.

The revolutionary atmosphere imposed, or at least encouraged, considerations of fraternité. Thus Delormel could claim that:

“in this revolutionary moment, when the human spirit, regenerating itself among the French people, leaps forward with renewed energy, is it too much to hope that perhaps [ . . . ] we might offer to the public a new language as well, a language that facilitates new discoveries by bringing students of various nations together, a language that serves as a common term for all languages, a language easy to grasp even for men with but a slight aptitude for instruction, a language, in short, which will soon make out of all the people of mankind a single, grand family? [ . . . ] The Light of Reason brings men together and thus reconciles them; this language, by facilitating its communication, will help to propagate that Light.” (pp. 48-50).

Each of the authors was aware of the objections made by the authors of the Encyclopédie; thus the a priori languages which they proposed were all ordered according to an encyclopedia-like structure, easy to understand and designed upon the model of the eighteenth century system of knowledge.

Gone was the grandiose pansophist afflatus that animated baroque encyclopedias; the criterion of selection was rather that of Leibniz: the inventors of the languages behaved as if they were conscientious librarians hoping to make consultation as easy as possible, without worrying whether or not their ordering corresponded to the theater of the world.

Absent as well was the search for “absolute” primitives; the fundamental categories were the large-scale divisions of knowledge; under these were listed dependent notions attached as sub-headings.

Delormel, for example, assigned different letters of the alphabet to several encyclopedic classes in a way reminiscent not so much of Wilkins as of the anonymous Spaniard–grammar, art of speech, states of things, correlatives, useful, pleasurable, moral, sensations, perception and judgement, passions, mathematics, geography, chronology, physics, astronomy, minerals, etc.”

“During the Enlightenment there began to develop a critical attitude towards any attempt to construct a system of a priori ideas. It was a critique founded, in large part, upon the considerations advanced by Leibniz.

Thus it was in terms that closely recalled Leibniz’s own description of an ideal library that, in his introduction to the Encyclopédie, d’Alembert was to sound the death knell for projects for philosophical a priori languages.

Presented with the practical problem of organizing an encyclopedia and justifying the way that it divided its material, the system of scientific knowledge began to take on the appearance of a labyrinth, a network of forking and twisting paths that put paid to any notion that knowledge might be represented in a tree diagram of any sort.

Knowledge might still be divided into branches, “some of which converge at a common center; and, since, starting from the center, it is impossible to follow all the branches at once, the choice [of pathway] is determined by the nature of the different intellects.”

The philosopher was whoever discovered the hidden passageways within that labyrinth, the provisional interconnections, the web of mutually dependent associations which constituted such a network as a geographical representation.

For this reason the authors of the Encyclopédie decided that each single article would appear as only one particular map, which, in its small way, might reflect the entire global map:

“objects approach each other more or less closely, presenting different aspects according to the perspective chosen by the particular geographer [ . . . ].

Thus it is possible to imagine that there are as many systems of human knowledge as there are representations of the world constructed according to differing projections [ . . . ].

Often, an object placed in one particular class on account of one or another of its properties may reappear in another class because of other properties.”

Following the suggestion of Locke, the Enlightenment was less concerned with the search for perfect languages than with the provision of therapies for already existing ones.

After denouncing the limits of natural languages, Locke (Essay, III, X) had passed to an analysis of the abuse which must occur whenever words are used that do not correspond to clear and distinct ideas, whenever they are used inconsistently, whenever they are employed with the affectation of obscurity, whenever words are taken for things, whenever they are used for things which possess no meaning, and whenever we imagine that others must necessarily associate with the words we use the same ideas as we do.

Locke fixed a set of norms to combat these abuses, and, since Locke was not concerned with lexical or syntactical reform, but simply with subjecting usage to a measure of vigilance and philosophical common sense, these norms had no bearing on the theme of philosophical languages.

Instead of a systematic reform of language, Locke modestly suggested that we be more conscientious in the way we use words to communicate with one another.

This was to be the line adopted by the encyclopedists of the Enlightenment and those whom they inspired.

The encyclopedists launched their attack on philosophical a priori languages principally in their entry under the heading “Caractère,” which was the result of the collaboration of several authors.

Du Marsais made an initial distinction between numerical characters, characters representing abbreviations, and literal characters; these last were further subdivided into emblematic characters (still the accepted interpretation of hieroglyphics) and nominal characters, primarily the characters of the alphabet.

D’Alembert accepted the criticisms that had traditionally been made of the characters used in natural languages, and then discussed the various projects for the construction of real characters, showing an extensive knowledge of the projects in the previous century.

It was a discussion which often confused characters that were ontologically real, that directly expressed, that is, the essence of the things they represented, with characters that were only logically real, capable, that is, of expressing by convention a single idea unequivocally. Still, d’Alembert advanced a number of criticisms that applied equally to both types.

In contrast to those of the seventeenth century, philosophers in the Enlightenment had radically changed the focus of their reflection on language. It now seemed clear that thought and language influenced each other, each proceeding with the other step by step, and that, consequently, language, as it evolved, would constantly modify thought.

Thus it no longer made sense to accept the rationalist hypothesis of a single grammar of thought, universal and stable, which all languages in one way or another reflected. No system of ideas postulated on the basis of abstract reasoning could thus ever form an adequate parameter of and criterion for the formation of a perfect language.

Language did not reflect a preconstituted mental universe, but collaborated in its growth.

The Idéologues demonstrated the impossibility of postulating a universal way of thinking, independent of the human semiotic apparatus. Destutt de Tracy (Eléments d’idéologie, I, 546, n.) argued that it was not possible to confer on all languages the attributes of algebra. In the case of natural languages:

“we are often reduced to conjectures, inductions, and approximations [ . . . ]. Almost never can we have a perfect certainty that an idea which we have constructed for ourselves under a certain sign and by various means is really utterly and entirely the same as the idea that those who taught us the sign as well as anyone else who might subsequently use the sign might attribute to it.

Hence words may often, insensibly, take on differences in meaning without anyone noting these changes; for this reason we might say that while every sign is perfectly transparent for whomever invents it, it is somewhat vague and uncertain for those who receive it [ . . . ].

I might even carry this further: I said that every sign is perfect for whomever invents it, but this is only really true at the precise instant when he invents the sign, for when he uses this same sign in another moment in his life, or when his mind is in another disposition, he can no longer be entirely sure that he has gathered up under this sign the same collection of ideas as he had the first time he used it.” (pp. 583-5).

Tracy understood that the prerequisite of all philosophical languages was the absolute and univocal correspondence between signs and the ideas they represented. An examination, however, of the seventeenth century English systems led him to the conclusion that “it is impossible that the same sign possess the same meaning for all who use it [ . . . ]. We thus must give up the idea of perfection.” (Eléments d’idéologie, II, 578-9).

This was a theme that was common to empiricist philosophy, to which all the Idéologues referred. Locke had already noted that although the names glory and gratitude were

“the same in every Man’s mouth, through a whole country, yet the complex, collective Idea, which everyone thinks on, or intends by that name, is apparently very different in Men using the same language. [ . . . ]

For though in the Substance Gold, one satisfies himself with Color and Weight, yet another thinks solubility in Aqua Regia, as necessary to be join’d with that Color in his Idea of Gold, as any one does its Fusibility; Solubility in Aqua Regia, being a Quality as constantly join’d with its Color and and Weight, as Fusibility, or any other; others put its Ductility or Fixedness, etc. as they had been taught by Tradition and Experience.

Who, of all these, has establish’d the right termination of the word Gold?” (Essay, III, IX, 8, 13).

The impossibility of elaborating a philosophic language is finally due to the fact that since languages develop through a set of stages, a development that the Idéologues delineated with great precision, there was no way of deciding the linguistic stage of development that a perfect language should represent.

Choosing to reflect one stage rather than another, a philosophical language will then continue to reflect all the limitations of that linguistic stage, while just to overcome these limitations humanity had passed to further and more articulate stages.

Once it had been perceived that the process of linguistic change is continuous, that language is subject to change not only at its prehistoric point of origin, but also in the present day, it became obvious that any thought of reviving the idea of a philosophic language was destined to fail.”

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“Thus all of the ingenuity expended upon the invention of philosophic a priori languages allowed Leibniz to invent a language of a radically different type, which–though remaining a priori–was no longer a practical, social instrument but rather a tool for logical calculation.

In this sense, Leibniz’s language, and the contemporary language of symbolic logic that descended from it, are scientific languages; yet, like all scientific languages, they are incapable of expressing the entire universe, expressing rather a set of truths of reason.

Such languages do not qualify as a universal language because they fail to express those truths that all natural languages express–truths of fact. Scientific languages do not express empirical events.

In order to express these we would need “to construct a concept which possesses an incalculable number of determinations,” while the completely determined concept of any individual thing or person implies “spatial-temporal determinations which, in their turn, imply other spatial-temporal successions and historical events whose mastery is beyond the human eye, and whose control is beyond the capacity of any man.” (Mugnai 1976: 91).

None the less, by anticipating what was to become the language of computers, Leibniz’s project also contributed to the development of programs well adapted for the cataloguing of the determinations of individual entities, which can tell us that there exists an entity called Mr. X such that this entity has booked a flight from A to B.

We may well fear that by controlling our determinations so well the computer eye has begun to infringe on our privacy, checking on the hour in which we reserved a room in a certain hotel in a certain city. This, then, is one of the side-effects of a project that commenced with the idea of expressing a merely theoretical universe populated with universal ideas such as goodness, angels, entity, substance, accidents, and “all the elephants.”

Dalgarno could never have imagined it. Passing through the mathematical filter of Leibniz, renouncing all semantics, reducing itself to pure syntax, his philosophical a priori language has finally managed to designate even an individual elephant.”

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The French Jesuit Joachim Bouvet (1656-1730) sent this unattributed diagram of hexagrams to Gottfried Wilhelm Leibniz (1646-1730) circa 1701. The arabic numerals written on the diagram were added by Leibniz. This artifact is held in the Leibniz Archive, Niedersächsische Landesbibliothek, and was published in Franklin Perkins, Leibniz and China: A Commerce of Light, Cambridge,2004, p. 117. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“Leibniz’s tendency to transform his characteristica into a truly blind calculus, anticipating the logic of Boole, is no less shown by his reaction to the discovery of the Chinese book of changes–the I Ching.

Leibniz’s continuing interest in the language and culture of China is amply documented, especially during the final decades of his life. In 1697 he had published Novissima sinica(Dutens 1768: IV, 1), which was a collection of letters and studies by the Jesuit missionaries in China.

It was a work seen by a certain Father Joachim Bouvet, a missionary just returned from China, who responded by sending Leibniz a treatise on the ancient Chinese philosophy which he saw as represented by the 64 hexagrams of the I Ching.

The Book of Changes had for centuries been regarded as a work of millennial antiquity. More recent studies, however, have dated it to the third century BCE. Nevertheless, scholars of the time of Leibniz still attributed the work to a mythical author named Fu Hsi.

As its function was clearly magical and oracular, Bouvet not unnaturally read the hexagrams as laying down the fundamental principles for Chinese traditional culture.

When Leibniz described to Bouvet his own research in binary arithmetic, that is, his calculus by 1 and 0 (of which he also praised the metaphysical ability to represent even the relation between God and nothingness), Bouvet perceived that this arithmetic might admirably explain the structure of the Chinese hexagrams as well.

He sent Leibniz in 1701 (though Leibniz only received the communication in 1703) a letter to which he added a wood-cut showing the disposition of the hexagrams.

Figure 14.1 shows the central structure of the diagrams seen by Leibniz. The sequence commences, in the upper left hand corner, with six broken lines, then proceeds by gradually substituting unbroken for broken lines.

Once again, the inclination of Leibniz was to void the Chinese symbols of whatever meaning was assigned to them by previous interpretations, in order to consider their form and their combinatorial possibilities.

Thus once more we find Leibniz on the track of a system of blind thought in which it was syntactic form alone that yielded truths. Those binary digits 1 and 0 are totally blind symbols which (through a syntactical manipulation) permit discoveries even before the strings into which they are formed are assigned meanings.

In this way, Leibniz’s thought not only anticipates by a century and a half Boole’s mathematical logic, but also anticipates the true and native tongue spoken by a computer–not, that is, the language we speak to it when, working within its various programs, we type expressions out on the keyboard and read responses on the screen, but the machine language programmed into it.

This is the language in which the computer can truly “think” without “knowing” what its own thoughts mean, receiving instructions and re-elaborating them in purely binary terms.

Certainly Leibniz mistook the nature of the I Ching, since “the Chinese interpreted the kua in every manner except mathematically” (Lozano 1971). Nevertheless, the formal structures that he (rightly enough) isolated in these diagrams appeared to him so esoterically marvelous that, in a letter to Father Bouvet, he did not hesitate in identifying the true author of the I Ching as Hermes Trismegistus–and not without reasons, because Fu Hsi was considered in China as the representative of the era of hunting, fishing and cooking, and thus can be considered, as can Hermes, the father of all inventions.”

“As Leibniz observed in the Accessio ad arithmeticum infinitorum of 1672 (Sämtliche Schriften und Briefen, iii/1, 17), when a person says a million, he does not represent mentally to himself all the units in that number. Nevertheless, calculations performed on the basis of this figure can and must be exact.

Blind thought manipulates signs without being obliged to recognize the corresponding ideas. For this reason, increasing the power of our minds in the manner that the telescope increases the power of our eyes, it does not entail an excessive effort.

“Once this has been done, if ever further controversies should arise, there should be no more reason for disputes between two philosophers than between two calculators. All that will be necessary is that, pen in hand, they sit down together at a table and say to each other (having called, if they so please, a friend) “let us calculate.” (In Gerhardt 1875: VII, 198ff).

Leibniz’s intention was thus to create a logical language, like algebra, which might lead to the discovery of unknown truths simply by applying syntactical rules to symbols. When using this language, it would no more be necessary, moreover, to know at every step what the symbols were referring to than it was necessary to know the quantity represented by algebraic symbols to solve an equation.

Thus for Leibniz, the symbols in the language of logic no longer stood for concrete ideas; instead, they stood in place of them. The characters “not only assist reasoning, they substitute for it.” (Couturat 1901: 101).

Dascal has objected (1978: 213) that Leibniz did not really conceive of his characteristica as a purely formal instrument apparatus, because symbols in his calculus are always assigned an interpretation. In an algebraic calculation, he notes, the letters of the alphabet are used freely; they are not bound to particular arithmetical values.

For Leibniz, however, we have seen that the numerical values of the characteristic numbers were, so to speak, “tailored” to concepts that were already filled with a content–“man,” “animal,” etc.

It is evident that, in order to demonstrate that “man” does not contain “monkey,” the numerical values must be chosen according to a previous semantic decision. It would follow that what Leibniz proposed was really a system both formalized and interpreted.

The system of notation, semicircles orientated in various ways, makes the characters hard to distinguish from one another; still, it was a system of notation that allowed for the representation of philosophical combinations such as “This Possible cannot be Contradictory.”

This language is, however, limited to abstract reasoning, and, like Lull, Richer did not make full use of the possibilities of combination in his system as he wished to reject all combinations lacking scientific utility (p. 55).

Towards the end of the eighteenth century, in a manuscript dating 1793-4, we also find Condorcet toying with the idea of a universal language. His text is an outline of mathematical logic, a langue des calculs, which identifies and distinguishes intellectual processes, expresses real objects, and enunciates the relations between the expressed objects and the intellectual operations which discover the enunciated relations.

The manuscript, moreover, breaks off at precisely the point where it had become necessary to proceed to the identification of the primitive ideas; this testifies that, by now, the search for perfect languages was definitively turning in the direction of a logico-mathematical calculus, in which no one would bother to draw up a list of ideal contents but only to prescribe syntactic rules (Pellerey 1992a: 193ff).

We could say that Leibniz’scharacteristica, from which Leibniz had also hoped to derive metaphysical truths, is oscillating between a metaphysical and ontological point of view, and the idea of designing a simple instrument for the construction of deductive systems (cf. Barone 1964: 24).

Moreover, his attempts oscillate between a formal logic (operating upon unbound variables) and what will later be the project of many contemporary semantic theories (and of artificial intelligence as well), where syntactic rules of a mathematical kind are applied to semantic (and therefore interpreted) entities.

But Leibniz ought to be considered the forerunner of the first, rather than of the second, line of thought.

The fundamental intuition that lies behind Leibniz’s proposal was that, even if the numbers were chose arbitrarily, even if it could not be guaranteed that the primitives posited for the same of argument were really primitive at all, what still guaranteed the truth of the calculus was the fact that the form of the proposition mirrored an objective truth.

Leibniz saw an analogy between the order of the world, that is, of truth, and the grammatical order of the symbols in language. Many have seen in this a version of the picture theory of language expounded by Wittgenstein in the Tractatus, according to which “a picture has logico-pictorial form in common with what it depicts” (2.2).

Leibniz was thus the first to recognize that the value of his philosophical language was a function of its formal structure rather than of its terms; syntax, which he called habitudo or propositional structure, was more important than semantics (Land 1974: 139).

“It is thus to be observed that, although the characters are assumed arbitrarily, as long as we observe a certain order and certain rule in their use, they give us results which always agree with each other. (Dialogus in Gerhardt 1875: VII, 190-3).

Something can be called an “expression” of something else whenever the structure [habitudines] subsisting in the expression corresponds to the structure of that which it wishes to express [ . . . ].

From the sole structure of the expression, we can reach the knowledge of the properties of the thing expressed [ . . . ] as long as there is maintained a certain analogy between the two respective structures.” (Quid sit idea in Gerhardt 1875: VII, 263-4).

What other conclusion could the philosopher of preestablished harmony finally have reached?”

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Johann Heinrich Lambert (1728-1777), Neues Organon, Leipzig, Johann Wendler, 1764. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“We have seen that Leibniz came to doubt the possibility of constructing an alphabet that was both exact and definitive, holding that the true force of the calculus of characteristic numbers lay instead in its rules of combination.

Leibniz became more interested in the form of the propositions generated by his calculus than in the meaning of the characters. On various occasions he compared his calculus with algebra, even considering algebra as merely one of the possible forms that calculus might take, and thought more and more of a rigorously quantitative calculus able to deal with qualitative problems.

One of the ideas that circulated in his thought was that, like algebra, the characteristic numbers represented a form of blind thought, or cogitatio caeca (cf. for example, De cognitione, veritate et idea in Gerhardt 1875: IV, 422-6). By blind thought Leibniz meant that exact results might be achieved by calculations carried out upon symbols whose meanings remained unknown, or of which it was at least impossible to form clear and distinct notions.

In a page in which he defined his calculus as the only true example of the Adamic language, Leibniz provides an illuminating set of examples:

“All human argument is carried out by means of certain signs or characters. Not only things themselves but also the ideas which those things produce neither can nor should always be amenable to distinct observation: therefore, in place of them, for reasons of economy we use signs.

If, for example, every time that a geometer wished to name a hyperbole or a spiral or a quadratrix in the course of a proof, he needed to hold present in his mind their exact definitions or manner in which they were generated, and then, once again, the exact definitions of each of the terms used in his proof, he would be likely to be very tardy in arriving at his conclusions. [ . . . ]

For this reason, it is evident that names are assigned to the contracts, to the figures and to various other types of things, and signs to the numbers in arithmetic and to magnitudes in algebra [ . . . ]

In the list of signs, therefore, I include words, letters, the figures in chemistry and astronomy, Chinese characters, hieroglyphics, musical notes, steganographic signs, and the signs in arithmetic, algebra, and in every other place where they serve us in place of things in our arguments.

Where they are written, designed, out sculpted, signs are called characters [ . . . ]. Natural languages are useful to reason, but are subject to innumerable equivocations, nor can be used for calculus, since they cannot be used in a manner which allows us to discover the errors in an argument by retracing our steps to the beginning and to the construction of our words–as if errors were simply due to solecisms or barbarisms.

The admirable advantages [of the calculus] are only possible when we use arithmetical or algebraic signs and arguments are entirely set out in characters: for here every mental error is exactly equivalent to a mistake in calculation.

Profoundly meditating on this state of affairs, it immediately appeared as clear to me that all human thoughts might be entirely resolvable into a small number of thoughts considered as primitive.

If then we assign to each primitive a character, it is possible to form other characters for the deriving notions, and we would be able to extract infallibly from them their prerequisites and the primitive notions composing them; to put it in a word, we could always infer their definitions and their values, and thereby the modifications to be derived from their definitions.

Once this had been done, whoever uses such characters in their reasoning and in their writing, would either never make an error, or, at least, would have the possibility of immediately recognizing his own (or other people’s) mistakes, by using the simplest of tests.” (De scientia universalis seu calculo philosophico in Gerhardt 1875: VII, 198-203).

This vision of blind thought was later transformed into the fundamental principle of the general semiotics of Johann Heinrich Lambert in his Neues Organon (1762) in the section entitled Semiotica (cf. Tagliagambe 1980).

“The idea of a universal encyclopedia was something that Leibniz was never to give up. Leibniz was, for a long period, a librarian; as such, and as a historian and érudit, he could not have failed to follow the pansophic aspirations and encyclopedic ferment that filled the closing years of the seventeenth century–tremors that would yield their fruits in the century to come.

For Leibniz, the interest in the idea of a universal encyclopedia grew less and less as the basis of an alphabet of primitive terms, and more and more as a practical and flexible instrument which might provide for everyone an access to and control over the immense edifice of human learning.

The point of departure was a rejection of Locke’s tripartite division of knowledge into physical, ethical and logical (or semiotic). Even such a simple classification was untenable, Leibniz argued, because every item of knowledge might reasonably be considered from more than one of the three divisions.

We might treat the doctrine of spirits either as a philosophical or as a moral problem, placing it in the province either of logic or of ethics. We might even consider that a knowledge of the spirit world might prove efficacious for certain practical ends; in which case we might want to place it in the physical province.

A truly memorable story might deserve a place in the annals of universal history; yet it might equally well deserve a place in the history of a particular country, or even of a particular individual. A librarian is often undecided over the section in which a particular book needs to be catalogued (cf. Serres 1968: 22-3).

Leibniz saw in an encyclopedia the solution to these problems. An encyclopedia would be a work that was, as we might now say, polydimensional and mixed, organized–as Gensini observes (Gensini 1990: 19)–more according to “pathways” than by a classification by subject matters; it would be a model of a practico-theoretical knowledge that invited the user to move transversally, sometimes following deductive lines, as mathematicians do, and sometimes moving according to the practical purposes of the human users.

It would be necessary also to include a final index that would allow the user to find different subjects or the same subject treated in different places from different points of view (IV, 21, De la division des sciences).

It is almost as if Leibniz intended here to celebrate as a felix culpa that monument of non-dichotomical incongruity that was the encyclopedia of Wilkins; as if he were writing a rough draft for the very project that d’Alembert was to set forth at the beginning of the Encyclopédie. Dimly shining from beneath the project of Wilkins, Leibniz has recognized the first idea of a hypertext.

“What did Leibniz’sars combinatoria have in common with the projects for universal languages? The answer is that Leibniz had long wondered what would be the best way of providing a list of primitives and, consequently, of an alphabet of thoughts or of an encyclopedia.

In the De organo sive arte magna cogitandi (Couturat 1903: 429-31) he even argued that “the greatest remedy for the mind consists in the possibility of discovering a small set of thoughts from which an infinity of other thoughts might issue in order, in the same way as from a small set of numbers [the integers from 1 to 10] all the other numbers may be derived.”

It was in this same work that Leibniz first made hints about the combinational possibilities of a binary calculus.

In the Consilium de Encyclopedia nova conscribenda methodo inventoria (Gensini 1990: 110-20) he outlined a system of knowledge to be subjected to a mathematical treatment through rigorously conceived propositions. He proceeded to draw up a plan of how the sciences and other bodies of knowledge would then be ordered: from grammar, logic, mnemonics topics (sic) and so on to morals and to the science of incorporeal things.

In a later text on the Termini simpliciores from 1680-4 (Grua 1948: 2, 542), however, we find him falling back to a list of elementary terms, such as “entity,” “substance” and “attribute,” reminiscent of Aristotle’s categories, plus relations such as “anterior” and “posterior.”

In the Historia et commendatio linguae characteristicae we find Leibniz recalling a time when he had aspired after “an alphabet of human thoughts” such that “from the combination of the letters of this alphabet, and from the analysis of the vocables formed by these letters, things might be discovered and judged.”

It had been his hope, he added, that in this way humanity might acquire a tool which would augment the power of the mind more than telescopes and microscopes had enlarged the power of sight.

Waxing lyrical over the possibilities of such a tool, he ended with an invocation for the conversion of the entire human race, convinced, as Lull had been, that if missionaries were able to induce the idolators to reason on the basis of the calculus they would soon see that the truths of our faith concord with the truths of reason.

Immediately after this almost mystical dream, however, Leibniz acknowledged that such an alphabet had yet to be formulated. Yet he also alluded to an “elegant artifice:”

“I pretend that these marvelous characteristic numbers are already given, and, having observed certain of their general properties, I imagine any other set of numbers having similar properties, and, by using these numbers, I am able to prove all the rules of logic with an admirable order, and to show in what way certain arguments can be recognized as valid by regarding their form alone.” (Historia et commendatio, Gerhardt 1875: VII, 184ff).

In other words, Leibniz is arguing that the primitives need only be postulated as such for ease of calculation; it was not necessary that they truly be final, atomic and unanalyzable.

In fact, Leibniz was to advance a number of important philosophical considerations that led him to conclude that an alphabet of primitive thought could never be formulated. It seemed self-evident that there could be no way to guarantee that a putatively primitive term, obtained through the process of decomposition, could not be subjected to further decomposition.

This was a thought that could hardly have seemed strange to the inventor of the infinitesimal calculus:

“There is not an atom, indeed there is no such thing as a body so small that it cannot be subdivided [ . . . ] It follows that there is contained in every particle of the universe a world of infinite creatures [ . . . ] There can be no determined number of things, because no such number could satisfy the need for an infinity of impressions.” (Verità prime, untitled essay in Couturat 1903: 518-23).

If no one conception of things could ever count as final, Leibniz concluded that we must use the conceptions which are most general for us, and which we can consider as prime terms only within the framework of a specific calculus.

With this, Leibniz’scharacteristica breaks its link with the research into a definitive alphabet of thought. Commenting on the letter to Mersenne in which Descartes described the alphabet of thoughts as a utopia, Leibniz noted:

“Even though such a language depends upon a true philosophy, it does not depend upon its perfection. This is to say: the language can still be constructed despite the fact that the philosophy itself is still imperfect.

As the science of mankind will improve, so its language will improve as well. In the meantime, it will continue to perform an admirable service by helping us retain what we know, showing what we lack, and inventing means to fill that lack.

Most of all, it will serve to avoid those disputes in the sciences that are based on argumentation. For the language will make argument and calculation the same thing.” (Couturat 1903: 27-8).

This was not only a matter of convention. The identification of primitives cannot precede the formulation of the lingua characteristica because such a language would not be a docile instrument for the expression of thought; it is rather the calculating apparatus through which those thoughts must be found.”

The point was to determine the number of truths capable of expression and the number of expressions capable of being put into writing. Given that Leibniz had found words of 31 letters in Latin and Greek, an alphabet of 24 letters would produce 2432 words of 31 letters.

But what is the maximum length of an expression? Why should an expression not be as long as an entire book? Thus the sum of the expressions, true or false, that a man might read in the course of his life, imagining that he reads 100 pages a day and that each page contains 1,000 letters, is 3,650,000,000.

Even imagining that this man can live one thousand years, like the legendary alchemist Artephius, it would still be the case that “the greatest expressible period, or the largest possible book that a man can read, would have 3,650,000,000,000 [letters], and the number of truths, falsehoods, or sentences expressible–that is, readable, regardless of pronounceability or meaningfulness–will be 24365,000,000,001 – 24/23 [letters].”

We can imagine even larger numbers. Imagine our alphabet contained 100 letters; to write the number of letters expressible in this alphabet we would need to write a 1 followed by 7,300,0000,000,000 (sic) zeros. Even to write such a number it would take 1,000 scribes working for approximately 37 years.

Leibniz’s argument at this point is that whatever we take the number of propositions theoretically capable of expression to be–and we can plausibly stipulate more astronomical sums than these–it will be a number that vastly outstrips the number of true or false expressions that humanity is capable of producing or understanding.

From such a consideration Leibniz concluded paradoxically that the number of expressions capable of formulation must always be finite, and, what is more, that there must come a moment at which humanity would start to enunciate them anew.

With this thought, Leibniz approaches the theme of the apochatastasis or of universal reintegration–what we might call the theme of the eternal return.

This was a line of speculation more mystical than logical, and we cannot stop to trace the influences that led Leibniz to such fantastic conclusions.

It is plain, however, that Leibniz has been inspired by Lull and the kabbala, even if Lull’s own interest was limited to the generation of just those propositions that expressed true and certain knowledge and he thus would never have dared to enlarge his ars combinatoria to include so large a number of propositions.

For Leibniz, on the contrary, it was a fascination with the vertiginous possibilities of discovery, that is of the infinite number of expressions of which a simple mathematical calculation permitted him to conceive, that served as inspiration.

Leibniz also elaborated in the Dissertatio his so-called method of “complexions,” through which he might calculate, given n elements, how many groups of them, taken t at a time, irrespective of their ordering, can be ordered.

He applied this method to syllogisms before he passed to his discussion of Lull (para. 56). Before criticizing Lull for limiting the number of his elements, Leibniz made the obvious observation that Lull failed to exploit all the possibilities inherent in his combinatorial art, and wondered what could happen with variations of order, which could produce a greater number.

We already know the answer: Lull not only limited the number of elements, but he rejected those combinations that might produce propositions which, for theological and rhetorical reasons, he considered false.

Leibniz, however, was interested in a logica inventiva (para. 62) in which the play of combinations was free to produce expressions that were heretofore unknown.

In paragraph 64 Leibniz began to outline the theoretical core of his characteristica universalis. Above all, any given term needed to be resolved into its formal parts, the parts, that is, that were explicitly entailed by its definition.

These parts then had to be resolved into their own components, and so on until the process reached terms which could not, themselves, be defined–that is, the primitives. Leibniz included among them not only things, but also modes and relations.

Other terms were to be classified according to the number of prime terms they contained: if they were composed from 2 prime terms, they were to be called com2nations; if from 3 prime terms, com3nations, and so forth. Thereby a hierarchy of classes of increasing complexity could be created.

Leibniz returned to this argument a dozen years later, in the Elementa characteristicae universalis. Here he was more generous with his examples. If we accept the traditional definition of man as “rational animal,” we might consider man as a concept composed of “rational” and “animal.”

We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate.

Given the preposition “all men are animals,” the number for the subject (men), is 6; the number for animals is 2; the resulting fraction is 6/2 = 3. Three being an integer, consequently, the preposition is true.

If the number for monkey were 10, we could demonstrate the falsity of either the proposition “all men are monkeys” or “all monkeys are men:” “the idea of monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6” (Elementa, in Couturat 1903: 42-92). These were principles that had all been prefigured in the Dissertatio.

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Johann Friedrich Wentzel (1670-1729), Gottfried Wilhelm Leibniz (1646-1716), circa 1700. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“In 1678 Leibniz composed a lingua generalis (in Couturat 1903). After decomposing all of human knowledge into simple ideas, and assigning a number to each, Leibniz proposed a system of transcription for these numbers in which consonants stood for integers and vowels for units, tens and powers of ten:

Umberto Eco, The Search for the Perfect Language, p. 270.

In this system, the figure 81,374, for example, would be transcribed as mubodilefa. In fact, since the relevant power of ten is shown by the following vowel rather than by the decimal place, the order of the letters in the name is irrelevant: 81,374 might just as easily be transcribed as bodifalemu.

This system might lead us to suspect that Leibniz too was thinking of a language in which the users might one day discourse on bodifalemu or gifeha (= 546) just as Dalgarno or Wilkins proposed to speak in terms of nekpot or deta.

Against this supposition, however, lies the fact that Leibniz applied himself to another, particular form of language, destined to be spoken–a language that resembled the latinosineflexione invented at the dawn of our own century by Peano.

This was a language whose grammar was drastically simplified and regularized: one declension for nouns, one conjunction for verbs, no genders, no plurals, adjectives and adverbs made identical, verbs reduced to the formula of copula + adjective.

Certainly, if my purpose were to try to delineate the entire extent of the linguistic projects undertaken by Leibniz throughout the course of his life, I would have to describe an immense philosophical and linguistically monument displaying four major aspects:

(1) the identification of a system of primitives, organized in an alphabet of thought or in a general encyclopedia;

(2) the elaboration of an ideal grammar, inspired probably by the simplifications proposed by Dalgarno, of which the simplified Latin is one example;

(3) the formulation of a series of rules governing the possible pronunciation of the characters;

(4) the elaboration of a lexicon of real characters upon which the speaker might perform calculations that would automatically lead to the formulation of true propositions.

The truth is, however, that by the end of his career, Leibniz had abandoned all research in the initial three parts of the project. His real contribution to linguistics lies in his attempts at realizing the fourth aspect.

Leibniz had little interest in the kinds of universal language proposed by Dalgarno and Wilkins, though he was certainly impressed by their efforts. In a letter to Oldenburg (Gerhardt 1875: VII, 11-5), he insisted that his notion of a real character was profoundly different from that of those who aspired to a universal writing modeled on Chinese, or tried to construct a philosophic language free from all ambiguity.

Leibniz had always been fascinated by the richness and plurality of natural languages, devoting his time to the study of their lineages and the connections between them. He had concluded that it was not possible to identify (much less to revive) an alleged Adamic language, and came to celebrate the very confusio linguarum that others were striving to eliminate (see Gensini 1990, 1991).

It was also a fundamental tenet of his monadology that each individual had a unique perspective on the world, as if a city would be represented from as many different viewpoints as the different positions of its inhabitants.

It would have been incongruous for the philosopher who held this doctrine to oblige everyone to share the same immutable grillwork of genera and species, without taking into account particularities, diversities and the particular “genius” of each natural language.

There was but one facet of Leibniz’s personality that might have induced him to seek after a universal form of communication; that was his passion for universal peace, which he shared with Lull, Cusanus and Postel.

In an epoch in which his english predecessors and correspondents were waxing enthusiastic over the prospect of universal languages destined to ease the way for future travel and trade, beyond an interest in the exchange of scientific information, Leibniz displayed a sensitivity towards religious issues totally absent even in high churchmen like Wilkins.

By profession a diplomat and court councillor, Leibniz was a political, rather than an academic, figure, who worked for the reunification of the church. This was an ecumenicism that reflected his political preoccupations; he envisioned an anti-French bloc of Spain, the papacy, the Holy Roman Emperor and the German princes.

Still, his desire for unity sprang from purely religious motives as well; church unity was the necessary foundation upon which a peaceful Europe could be built.

Leibniz, however, never thought that the main prerequisite for unity and peace was a universal tongue. Instead, he thought that the cause of peace might be better served by science, and by the creation of a scientific language which might serve as a common instrument in the discovery of truth.”

“This idea of a non-hierarchical organization seems, at one point, to have occurred to Wilkins as well. Figure 13.2 reproduces a table found on p. 311 of his Essay. The table describes the workings of prepositions of motion by relating the possible positions (and possible actions) of a human body in a three-dimensional space.

It is a table in which there is no principle of hierarchy whatsoever. Yet this is an isolated example, and Wilkins seems to have lacked the courage to extend this principle to his entire system of content.

Unfortunately, even Lodwick’s primitives for actions were not really primitive at all. It would undoubtedly be possible to identify a series of positions assumed by the human body in space–such as getting up or lying down–and argue that these were intuitively and universally comprehensible; yet the sixteen radicals proposed by Lodwick can be criticized in the same way as Degérando would later do for Wilkins: even such a simple notion as to walk must be defined in terms of movement, the notion of movement requires as its components those of place, of existence in a given place, of a moving substance which in different instants passes from one place to another.

All this presupposes the notions of departure, passage and arrival, as well as that of a principle of action which imparts motion to a substance, and of members which support and convey a body in motion in a specific way (“car glisser, ramper, etc., ne sont pas la même chose que marcher;” “since sliding, climbing, etc., are not the same as walking;” Des signes, IV, 395).

Moreover, it is also necessary to conceive of a terrestrial surface upon which movement was to take place–otherwise one could think of other actions like swimming or flying. However, at this point one should also subject the ideas of surface or members to the same sort of regressive componential analysis.

One solution would be to imagine that such action primitives are selected ad hoc as metalinguistic constructs to serve as parameters for automatic translation. An example of this is the computer language designed by Schank and Abelson (1977), based on action primitives such as PROPEL, MOVER, INGEST, ATRANS OR EXPEL, by which it is possible to analyze more complex actions like to eat (however, when analyzing the sentence “John is eating a frog,” Schank and Abelson–like Lodwick–cannot further analyze frog).

Other contemporary semantic systems do not start by seeking a definition of a buyer in order to arrive eventually at the definition of the action of buying, but start rather by constructing a type-sequence of actions in which a subject A gives money to a subject B and receives an object in exchange.

Clearly the same type-sequence can be employed to define not only the buyer, but also the seller, as well as the notions of to buy, to sell, price, merchandise, and so forth. In the language of artificial intelligence, such a sequence of actions is called a “frame.”

A frame allows a computer to draw inferences from preliminary information: if A is a buyer, then he may perform this and that action; if A performs this or that action, then he may be a buyer; if A obtains merchandise from B but does not pay him, then A is not a guyer, etc., etc.

In still other contemporary semantics, the verb to kill, for example, might be represented as “Xs causes (Xd changes to (- live Xd)) + (animate Xd) & (violent Xs):” if a subject (s) acts, with violent means or instruments, in a way that causes another subject (d), an animate being, to change from a state of living to a state of death, then s has killed d. If we wished, instead, to represent the verb to assassinate, we should add the further specification that d is not only an animate being, but also a political person.

It is worth noting that Wilkins‘ dictionary also includes assassin, glossing it by its synonym murther (erroneously designating it as the fourth species of the third difference in the genera of judicial relations: in fact, it is the fifth species), but limiting the semantic range of the term by “especially, under pretence of Religion.”

It is difficult for a philosophic a priori language to follow the twists and turns of meaning of a natural language.

Properly worked out, Lodwick’s project might represent to assassinate by including a character for to kill and adding to it a note specifying purpose and circumstances.

Lodwick’s language is reminiscent of the one described by Borges in “Tlön, Uqbar, Orbis Tertius” (in Ficciones), which works by agglutinations of radicals representing not substances but rather temporary fluxes. It is a language in which there would be no word for the noun moon but only the verb to moon or to moondle.

Although it is certain that Borges knew, if only at second hand, the work of Wilkins, he probably had never heard of Lodwick. What is certain, however, is that Borges had in mind the Cratylus, 396b–and it is by no means impossible that Lodwick knew this passage as well.

Here Plato, arguing that names are not arbitrary but motivated, gives examples of the way in which, rather than directly representing the things that they designate, words may represent the origin or the result of an action.

For instance, the strange difference (in Greek) between the nominative Zeus and the genitive Dios arose because the original name of Jupiter was a syntagm that expressed the habitual activity associated with the king of the gods: di’hoòn zen, “He through whom life is given.”

Other contemporary authors have tried to avoid the contortions that result from dictionary definitions by specifying the meaning of a term by a set of instructions, that is, a procedure which can decide whether or not a certain word can be applied.

This idea had already appeared in Charles Sanders Pierce (Collected Papers, 2.330): here is provided a long and complex explanation of the term lithium, in which this chemical element was defined not only in relation to its place in the periodic table of elements and by its atomic weight, but also by the operations necessary to produce a specimen of it.

Lodwick never went as far as this; still, his own intuition led him to run counter to an idea that, even in the centuries to follow, proved difficult to overcome. This was the idea that nouns came first; that is, in the process in which language had emerged, terms for things had preceded terms for actions.

Besides, the whole of Aristotelian and Scholastic discussion privileged substances (expressed by common nouns) as the subjects of a statement, in which the terms for actions played the role of predicates.

We saw in chapter 5 that, before the advent of modern linguistics, theorists tended to base their research on nomenclature. Even in the eighteenth century, Vico could still assume that nouns arose before verbs (Scienza nuova seconda, II, 2.4). He found this to be demonstrated not only by the structure of a proposition, but by the fact that children expressed themselves first in names and interjections, and only later in verbs.

Without following Stankiewicz’s reconstruction step by step, it is worth noting that the reevaluation of the role of the verb was assumed in the comparative grammars by the theorists of the Indo-European hypothesis, and that in doing so they followed the old tradition of Sanskrit grammarians, who derived any word from a verbal root (1974: 176).

We can close with the protest of De Sanctis, who, discussing the pretensions of philosophic grammars, criticized the tradition of reducing verbs to nouns and adjectives, observing that: “I love is simply not the same as I am a lover [ . . . ] The authors of philosophical grammars, reducing grammar to logic, have failed to perceive the volitional aspect of thought” (F. De Sanctis, Teoria e storia della litteratura, ed. B. Croce, Bari: Laterza, 1926: 39-40).

In this way, in Lodwick’s dream for a perfect language there appears the first, timid and, at the time, unheeded hint of the problems that were to become the center of successive linguistics.”

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Francis Lodwick (1619-1694), eight verses from the first chapter of the Gospel of St. John in Francis Lodwick’s common writing, next to the numerical key composed for it. A Common Writing, London, 1647. Museum of the History of Science, University of Oxford. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

Lodwick was not a learned man–no more than a merchant, as he humbly confessed. Though, in his Ars signorum, Dalgarno praised Lodwick for his endeavors, he was unable to hold back the supercilious observation that he did not possess the force adequate so such an undertaking, being a man of the arts, born outside of the Schools (p. 79).

In his writings, Lodwick advanced a number of proposals, some more fruitful than others, on how to delineate a language that would both facilitate commercial exchange and permit the easy acquisition of English.

His ideas, moreover, changed over time, and he never managed to design a complete system. None the less, certain of what appears in the most original of his works (A Common Writing, hardly thirty pages long) reveals him as striking off in a direction very different from other authors of his time, making him a precursor of certain trends of contemporary lexical semantics.

In theory, Lodwick’s project envisioned the creation of a series of three numbered indexes; the purpose of these was to refer English words to the character and these to its words. What distinguished Lodwick’s conception from those of the polygraphers, however, was the nature of its lexicon.

Lodwick’s idea was to reduce the number of terms contained in the indexes by deriving as many of them as possible from a finite number of primitives which express actions. Figure 13.1 shows how Lodwick chooses a conventional character (a sort of Greek delta) to express the action of drinking; then, by adding to this radix different grammatical marks, makes the different composite characters express ideas such as the actor (he who drinks), the act, the object (that which is drunk), the inclination (the drunkard), the abstraction, and the place (the drinking house, or tavern).

From the time of Aristotle up until Lodwick’s own day, names of substances had invariably been the basis upon which a structure of classification had been erected. Lodwick’s original contribution, however, was to commence not with substantives but with verbs, or schemes of actions, and to populate these schemes with roles–what we would now call actants–such as agent, object, place and so on.

Lodwick designed his characters to be easily recognized and remembered: as we have seen, to drink was specified by a sort of Greek delta, while to love was a sort of L. The punctuation and added notes are vaguely reminiscent of Hebrew. Finally, as Salmon suggests, Lodwick probably took from contemporary algebra the idea of substituting letters for numbers.

In order to set up his finite packet of radicals Lodwick devised a philosophical grammar in which even grammatical categories expressed semantic relations. Derivatives and morphemes could thus become, at the same time, criteria of efficiency to reduce each grammatical category further to a component of action.

By such means the number of characters became far small than the words of a natural language found in a dictionary, and Lodwick endeavored to reduce this list further by deriving his adjectives and adverbs from the verbs.

From the character to love, for example, he derived not only the object of the action (the beloved) but also its mode (lovingly); by adding a declarative sign to the character to cleanse, he asserted that the action of cleansing has been performed upon the object–thereby deriving the adjective clean.

Lodwick realized, however, that many adverbs, prepositions, interjections and conjunctions were simply not amenable to this sort of derivation; he proposed representing these as notes appended to the radicals. He decided to write proper names in natural languages.

He was embarrassed by the problem of “natural kinds” (let us say, names of substances like cat, dog, tree), and resigned himself to the fact that, here, he would have to resort to a separate list. But since this decision put the original idea of a severely limited lexicon in jeopardy, he tried to reduce the list of natural kinds as much as possible, deciding that terms like hand, foot or land could be derived from actions like to handle, to foot or to land.

In other cases, he resorted to etymology, deriving, for instance, king from the archaic radical to kan, claiming that it meant both to know and to have power to act. He pointed out that Latin rex was related to the verb regere, and suggested that both the English king and the German emperor might be designated by a simple K followed by the name of the country.

Where he was not able to find appropriate verbal roots, he tried at least to reduce as many different sounds as possible to a single root. He thus reduced the names for the young of animals–child, calfe, puppy, chikin–to a single root.

Moreover, Lodwick thought that the reduction of many lexical items to a unique radical could also be performed by using analogies (seeing as analogous to knowing), synonymy (to lament as a synonym of tobemoane), opposition (to curse as the opposite of to bless), or similarities in substance (to moisten, to wet, to wash and even to baptize are all reduced to moisture).

All these derivations were to be signaled by special signs. Wilkins had had a similar idea when proposing the method of transcendental particles, but it seems that Lodwick’s procedure was less ambiguous.

Lodwick barely sketched out his project; his system of notation was cumbersome; nevertheless (with a bare list of sixteen radicals–to be, to make, to speake, to drinke, to love, to cleanse, to come, to begin, to create, to light, to shine, to live, to darken, to comprehend, to send and to name), he managed to transcribe the opening of the gospel of St. John (“In the Beginning was the Word, and the Word was with God . . .”).

Beginning was derived of course from to begin, God from to be, Word from to speake, and so on (the idea of all things is derived from to create).

Just as the polygraphers had taken Latin grammar as a universal model, so Lodwick did the same for English–though his English grammatical categories still reflected the Latin model. Nevertheless he succeeded in avoiding certain limits of the Aristotelian classification of substances, because no previous tradition obliged him to order an array of actions according to the rigid hierarchical schema requested by a representation of genera and species.”

“What if we regarded the defect in Wilkins‘ system as its prophetic virtue? What if we treated Wilkins as if he were obscurely groping towards a notion for which we have only recently invented a name–hypertext?

A hypertext is a program for computers in which every node of element of the repertory is tied, through a series of internal references, to numerous other nodes. It is possible to conceive of a hypertext on animals where, starting from the unit dog, one can get information (1) on the place of dogs on a tree of biological taxa which comprises also cats, horses or wolves; (2) on the properties and habits of dogs; (3) on dogs in history (the dog in the Neolithic, dog in medieval castles, etc.); (4) on the image of the dog in great works of art; and so on.

In the end, this was perhaps what Wilkins really wanted to do when he considered defence from the perspective both of the duties of a citizen and of military strategy.

If this were the case, many of the system’s contradictions would disappear, and Wilkins could be considered as a pioneer in the idea of a flexible and multiple organization of complex data, which will be developed in the following century and in those after.

Yet, if such was his project, then we can no longer speak of him in the context of the search for a perfect language; his was instead the search for ways to articulate all that natural languages permit us to say.”

“Let us try to understand a little better what is happening here. Suppose we wanted to use the real character to understand the difference between a dog and a wolf. We discover only that the dog, Zitα, is the first member of the first specific pair of the fifth difference of the genus Beasts, and that the wolf Zitαs, is the opposing member of this pair (s being the character for specific opposition).

But in this way the character says what is the position of a dog in a universal classification of beasts (which, like Fish and Bird are animate sensitive sanguineous substances), without providing information either on the physical characteristics of dogs or on the difference between a dog and a wolf.

To learn more about dogs and wolves we must read further in the tables. Here we can learn (1) that clawed viviparous animals have toes at the end of their feet; (2) that rapacious viviparous animals have generally “six short pointed incisors, or cutting teeth, and two long fangs to hold their prey;” (3) that the head of dog-kind beasts is oblong, while the head of cat-kind animals is roundish; (4) that the larger of the dog-kind fall into two further groups–“either that which is noted for tameness and docility; or for wildness and enmity to sheep.”

With this, we finally know the difference between a dog and a wolf.

Thus genera, differences and species only serve to “taxonomize” entities rather than to define the properties by which we recognize them. To make these properties evident it is necessary to attach a running commentary to the classification.

Within Aristotelian classification, defining man as a rational animal was perfectly adequate. But this is not adequate for Wilkins, for he lived in an age that wished to discover the physical and biological nature of things.

He thus needed to know what were the morphological and behavioral characteristics of dogs as well. Yet his tables only allowed him to express this information in the form of additional properties and circumstances, and this additional information had to be expressed in natural language because the characteristic language lacked the formulae to render it evident.

This consecrates the failure of Wilkins‘ project, considering that, according to his project, “we should, by learning the Character and the Names of things, be instructed likewise in their Natures” (p. 21).

One might wish at least to call Wilkins a pioneer of modern, scientific taxonomy (like the taxonomy shown in figure 10.3). Yet, as Slaughter has noted, he has lumped together the pre-scientific taxonomies and folk taxonomy.

To classify, as we usually do, onions and garlic as foodstuffs and lilies as flowers is an instance of folk taxonomy: from a botanical point of view, onions, garlic and lilies are all members of the Liliaceae family.

See how Wilkins, when he classifies dogs, starts out using morphological criteria, then goes on mixing functional and even geographical criteria.

What, then, is that character Zitα that tells us so little about dogs, forcing us to learn more by inspecting the tables? One might compare it with a pointer which permits access to information stored in the computer’s memory–and which is not provided by the form of the character itself.

The speakers who wished to use the characteristic language as their natural idiom should have already memorized all that information in order to understand the character. But that is exactly the same type of competence requested of speakers who, instead of Zitα, say cane, dog, per or Hund.

For this reason, the encyclopedic information that underlies the list of primitives negates the compositional principle of Wilkins‘ language. Wilkins‘ primitives are not primitives at all. His species do not emerge from the composition of genera and differences alone; they are also names used as pegs to hang up encyclopedic descriptions.

Moreover, not even genera and differences are primitive, since they can be defined only through encyclopedic definitions. They neither are innate notions, nor can be immediately grasped by intuition: if one could still say so of the ideas of “God” or “world,” one would hardly do so for, let us say, “naval and ecclesiastical relations.”

Genera and differences are not primitive notions because–if they were–they should be definable by nature, while the tables are conceived just in order to define them by means of a natural language, Wilkins‘ English.

If Wilkins‘ classification were logical consistent, it should be possible to assume that it is analytically true that the genus of Beasts entails Animate Substance, which in its turn entails Creatures Considered Distributively.

Even this, in fact, is not always the case. The opposition vegetative / sensitive, for example, in the table of genera serves to distinguish Stone and Tree (and has an uncertain status); but the same opposition reappears (not once but twice) in the table of the World (see figure 12.6, where repeated terms are in bold).

Thus, on the basis of figure 12.1, one should admit that everything vegetative is necessarily an animate creature, while according to figure 12.6, one should (rather contradictorily) admit that everything vegetative is necessarily an element of both the spiritual and the corporeal world.

It is obvious that these various entities (be they genera, species or whatever) are considered under a different point of view every time they appear in the tables. Yet, in this case, we are no longer confronting a classification whose purpose is to construct a tree of organized terms in which every entity is unequivocally defined by the place it holds within the classification; we are, instead, confronting a great encyclopedia in which it is only expected that the same topics will be treated from more than one point of view in different articles.

Consulting the table for Economic Relations, we find, among its species, the pair Defending versus Deserting. If we turn to the table for Military Relations we still find Defense; though this time it is opposed to Offense.

It is true that when defense is considered as an economic relation and the opposite of desertion, it is written Coco, while considered as a type of military action, the opposite of offense, it is written Sibα.

Thus two different characters denote two different notions. Yet are they really different notions rather than one notion considered from two viewpoints? As a matter of fact, the ideas of economic defence and military defence seem to have something in common.

In both cases we are facing an act of war, which is seen the first time as a patriotic duty and the second time as a response to the enemy. The fact that the two notions are conceptually related, however, implies that within the structure of pseudo-dichotomies there also exist transversal connections, linking the nodal points in different sections of the tree.

Yet is such connections exist, then the tree is no more a hierarchical tree; it is rather a network of interrelated ideas.

“Division differs from classification in that the latter bases itself upon the intimate properties of the objects it wishes to distribute, while the former follows a rule to a certain end to which these objects are destined.

Classification apportions ideas into genera, species, and families; division allocates them into regions of greater or lesser extent. Classification is the method of botanists; division is the method by which geography is taught.

If one wishes for an even clearer example, when an Army is drawn up in battle formation, each brigade under its general, each battalion under its commander, each company under its captain, this is an image of division; when, however, the state of this army is presented on a role, which principally consists of en enumeration of the officers of each rank, then of the subalterns, and finally of the soldiers, this is an image of classification (IV, 399-400).”

Degérando is doubtlessly thinking here of Leibniz’s notion of the ideal library and of the structure of the Encyclopédie of which we will later speak), that is, of a criterion for subdividing matter according to the importance that it has for us.

Yet a practical classification follows criteria different from those which should rule a system of primitives based on metaphysical assumptions.”

“Using 40 genera and 251 differences, Wilkins‘ tables manage to define 2,030 species. If, however, the division were dichotomic, as happens with the Aristotelian system of classification, in which each genus was assigned two decisive differences which constituted to new species below, and in which each of these new species then played the role of genera at the lower level in the process of dichotomization, there should have been at least 2,048 species (as well as 1,025 intermediary genera plus the category at the apex) and an equal number of differences.

If the figures do not add up in the way that they should, it is clear that, in reconstructing a single general tree from the 41 particular trees represented in the tables, one would not find a constant dichotomic structure.

The structure is not dichotomic because Wilkins mixes substances and accidents together; but since, as Dalgarno had recognized, the number of accidents is infinite, there is no way that they can be hierarchically ordered.

In fact, Wilkins must classify fundamental and Platonic conceptions, like God, world or tree, together with drinks, like beer, political offices, military and ecclesiastical ranks–in short, the whole notional world of a seventeenth century Englishman.

It suffices to look at figure 12.1 to see that the accidents are subdivided into five categories each yielding from three to five genera. There are three subdivisions of the genus Herb as well as of the genus Transcendental things.

With a dichotomic structure it would be easy, once having established the number of embedded levels, to control the total number of entities in the system; once the pattern has been broken, however, and more than two subdivisions allowed to appear at each nodal point, the whole system begins to spin out of control.

The system is open to new discoveries, but, at the same time, surrenders its control over the number of primitives.

When he reaches the last differences, Wilkins arranges them in pairs. Yet, as he is the first to recognize, he has made his arrangement “for the better helming of the memory” (p. 22), not according to a rigorous criterion of opposition.

He informs us that pairs are based sometimes on opposition and sometimes on affinity. He admits to having coupled his differences in an arguable way, but says that he did so “because I knew not to provide for them better” (p. 22).

For instance, in the first genus, General Transcendental, the third difference, Diversity, generates as the second of its species Goodness and its opposite, Evil; but the second difference, Cause, generates as its third species Example and Type.

These two categories are not opposed; in fact it is not clear what their relation to each other is. We can imagine some sort of relation of affinity or similarity; yet, in whatever case, the criterion seems weak and ad hoc.

Among the accidents of Private Relations, under the species Economical Relations, we find both Relations of Consanguinity (like Progenitor / Descendant, Brother / Half-Brother, Coelebs / Virgin–but Coelebs has among its synonyms both Bachelour and Damosel, while Virgin only Maid) and Relations of Superiority (Direct / Seduce, Defending / Deserting).

It is clear that all of these oppositions lack a constant criterion. Among the same PrivateRelations there are also the Provisions, which includes pairs such as Butter / Cheese, but also actions such as Butchering / Cooking and Box / Basket.

It is hardly by chance that Wilkins is repeatedly forced to justify his language on mnemonic grounds. In fact, Wilkins takes some of his procedures from the traditional arts of memory.

His criterion for establishing pairs is based on the most common mnemonic habits. Rossi (1960: 252) notes that Wilkins‘ botanist, John Ray, complained that he was not permitted to follow the commandments of nature, but rather the exigencies of regularity, almost as if he were forced to adapt his classification more to requirements of the traditional theaters of memory than to the canons of modern taxonomies.

Nor is it even clear what, in the tree of genera (figure 12.1), the subdivisions in lower case actually mean. They cannot be differences, because the differences appear later, in successive tables, and determine how, in each of the 40 major genera, the dependent species are to be generated.

Some of these lower-case entities seem to serve as super-genera; yet others appear in an adjectival form. Certain of these latter look like differences in the Aristotelian tradition–like animate / inanimate, for example. We might regard them as pseudo-differences.

However, if the generative path “substances + inanimate = ELEMENTS” seems to follow an Aristotelian criterion, the disjunctions after animate are established in a quite different fashion.

Animate substances are divided into parts and species, the species are divided into vegetative and sensitive, the vegetative species into imperfect and perfect, and it is only at the end of these disjunctions that it is possible to isolate genera like Stone or Metal.

This is not the only instance of this sort of confusion. Moreover, given a pair of opposed categories, such as Creator / creature, the first term of the division is a genus, but the second appears as a pseudo-difference through which, after other disjunctions, it is possible to isolate other genera.

Likewise, in the group Herb, Shrub and Tree, the last two are genera; the first is a sort of super-genus (or pseudo-difference) subdivided into three further genera.

It would be nice, Wilkins confessed (p. 289), if each of his differences had its own transcendental denomination; yet there did not seem to be sufficient terms in the language for this.

He admitted as well that while, in theory, a well-enough individuated difference would immediately reveal the form which gave the essence to each thing, these forms remained largely unknown.

So he had to content himself by defining things through properties and circumstances.”

“In reality, Wilkins’ classification ought to be regarded as an open one. Following a suggestion of Comenius‘ (in the Via lucis), Wilkins argued that the task of constructing an adequate classification could only be undertaken by a group of scientists working over a considerable period of time, and to this end he solicited the collaboration of the Royal Society.

The Essay was thus considered no more than a first draft, subject to extensive revision. Wilkins never claimed that the system, as he presented it, was finished.

Looking back at figures 12.3 and 12.4, it is evident that there are only nine signs or letters to indicate either differences or species. Does this mean that each genus may have no more than nice species? It seems that the number nine had no ontological significance for Wilkins, and that he chose it simply because he thought nine was the maximum number of entities that might easily be remembered.

He realized that the actual number of species for each genus could not be limited. In fact, certain of the genera in the tables only have six species, but there are ten species for the Umbelliferous and seventeen for the Verticillates Non Fruticose.

To accommodate genera with over nine species Wilkins invented a number of graphic artifices. For simplicity’s sake, let us say that, in the spoken language, to specify a second group of nine species an l is added after the first consonant of the name, and that to specify a third group an r is added.

Therefore if Gαpe is normally Tulip (third species of the fourth difference of the genus Herbs according to their leaves), then Glαpe will be Ramsom, because the addition of the l means that the final e no longer indicates the third species in the genus but the twelfth.

Yet is precisely at this point that we come across a curious error. In the example we just gave, we had to correct Wilkins‘ text (p. 415). The text uses the normal English terms Tulip and Ramsom, but designates them in characters by Gαde and Glαde rather than Gαpe and Glαpe (as it should be).

If one checks carefully on the tables, one discovered that Gαde denotes Barley, not Tulip. Wilkins‘ mistake can be easily explained: regardless of whatever botanical affinities the plants might possess, in common English, the words Tulip and Barley are phonetically dissimilar, and thus unlikely to ever be confused with each other.

In a philosophical language, however, members of the same species are easy to muddle either phonetically or graphically. Without constant double-checking against the tables, it is difficult to avoid misprints and misunderstandings.

The problem is that in a characteristic language, for every unit of an expression one is obliged to find a corresponding content-unit. A characteristic language is thus not founded–as happens with natural languages–on the principle of double articulation, by virtue of which meaningless sounds, or phonemes, are combined to produce meaningful syntagms.

This means that in a language of “real” characters any alteration of a character (or of the corresponding sound) entails a change of sense.

This is a disadvantage that arises from what was intended as the great strength of the system, that is, its criterion of composition by atomic features, in order to ensure a complete isomorphism between expression and content.

Flame is Debα, because here the α designates a species of the element Fire. If we replace the α with an a we obtain a new composition, Deba, that means Comet. When designing his system, Wilkins‘ choice of α and a was arbitrary; once they are inserted into a syntagm, however, the syntagmatic composition is supposed to mirror the very composition of the denoted thing, so that “we should, by learning the Character and the Names of things, be instructed likewise in their Natures” (p. 21).

This creates the problem of how to find the name for yet unknown things. According to Frank (1979: 80), Wilkins‘ language, dominated by the notion of a definitively pre-established Great Chain of Being, cannot be creative. The language can name unknown things, but only within the framework of the system itself.

Naturally, one can modify the tables by inserting into them a new species, but this presupposes the existence of some sort of linguistic authority with the power to permit us to think of a new thing. In Wilkins’s language neologisms are not impossible, but harder to form than in natural languages (Knowlson 1975: 101).

One might defend Wilkins‘ language by arguing that it really encompasses a rational methodology of scientific research. If, for example, we were to transform the character Detα (rainbow) into Denα we would obtain a character that we could analyze as denoting the first species of the ninth difference of the genus Element.

Yet there is no such species in the tables. We cannot take the character metaphorically, because only characters followed by transcendental particles may be so interpreted. We can only conclude that the character unequivocally designates an as yet to be discovered content, and that even if the content remains undiscovered, the character has at least told us the precise point where it is to be found.

But what and where is that “point?” If the tables were analogous to the periodic table in chemistry, then we really would know what to look for. The periodic table contains boxes which, though momentarily empty, might, one day, be filled.

Yet the language of chemistry is rigorously quantitative; the table gives the atomic number and weight of each missing element. An empty space in Wilkins‘ classification, however, merely tells us that there is a hole at that point; it does not tell us what we need to fill it up, or why the hole appears in one space rather than another.

Since Wilkins‘ language is not based on a rigorous classification, it cannot be used as a procedure of scientific discovery.”

“Wilkins‘ language provides names for 2,030 primitives, that is to say, species. These species include not only natural genera and artifacts, but also relations and actions. From these latter are derived the verbs.

As in Dalgarno, Wilkins used the copula + adjective formula for verbs, so “I love” is, again, “I am lover.” Besides this, the grammatical particles allow for the expression of tenses and modes for the verbs to be and to have as well as for pronouns, articles, exclamations, prepositions, conjunctions; the accidental differences express number, case, gender and comparatives.

But 2,030 primitive terms is still far too few to support discourse on a wide enough variety of topics. To increase the range of his language, Wilkins provided at the end of his Essay a list of 15,000 English terms not directly represented in his language, indicating the way that these might still be expressed.

The first way was by synonyms. For terms not included among the original 2,030, the list seeks to find the semantically closest primitive. To translate Result, the list suggests using primitive terms such as Event, Summe or Illation, without specifying in which context one should use the most appropriate synonym.

The list of possible synonyms can sometimes be very complex; for CorruptionWilkins suggests Evil, Destruction, Spoiling, Infection, Decay or Putrefaction. Some lists are even comic, as in the sequence of synonyms box-chest of drawers-ark-dresser-coffin-table.

The second way is periphrasis. The final dictionary records the term Abbie which has no corresponding primitive. There are primitives, however, for both Colledge and Monk. Thus, through periphrasis, Abbie can be rendered as Colledge of Monks.

The third way is that of the so-called transcendental particles. Faithful to his conception of a componential semantics based on primitive terms, Wilkins argued that there was no need to provide an additional character for Calf, since it is possible to express the same concept through Cow + Young, nor a primitive for Lioness when there was both a primitive for Lion and a marker for the feminine gender.

Thus in his grammar, Wilkins provided a system of transcendental particles (which then become a system of special markers for writing and pronunciation) that amplified or changed the meaning of the characters to which they were linked.

The 48 particles were articulated into eight classes, though there was little system in the classification. In fact, Wilkins drew from the Latin grammar the idea of different terminations such as “inceptives” (lucesco, aquosus, homunculus), “segregates” (gradatim or verbatim), endings indicating place (vestiarium) or agent (arator).

Sometimes these markers were essentially grammatical; as happens with those of gender, but for others Wilkins also took into account rhetorical devices such as metaphor, metonymy and synecdoche.

The particles in the class “metaphorical-like” indicate that the terms to which they are apposited are to be taken in a figurative sense. In this way, the primitive root can be modified so as to mean original, or light to mean evident.

Other particles seem to indicate relations such as cause and effect, container and thing contained, function and activity. Here are a few examples:

like + foot = pedestal

like + dark = mystical

place + metal = mine

officer + navy = admiral

artist + star = astronomer

voice + lion = roaring

Unfortunately, this incorporation of rhetorical solutions adds an element of imprecision to the entire system, and this weakens the project as a whole. Although Wilkins gave a list of examples showing the correct use of the particles, he was forced to acknowledge that they were just examples.

This list remains open, and its further elaboration is left to the inventiveness of the individual speaker (p. 318). Once set the speaker free to invent, and it is hard to avoid the risk of ambiguity.

Still, it is important to observe that–if the presence of a particle can produce ambiguity–its absence proves without any shade of doubt that a given term must be taken literally. This represents an advance of Dalgarno, in whose system there was nothing to indicate when terms should be understood literally or figuratively.

The fact is that Wilkins the author of a philosophical grammar seems to be working against Wilkins the inventor of a philosophic a priori language in real characters. Wilkins‘ attempt to take into account the figurative side of language also is certainly an interesting effort; however, it affects the precision of his language and its original claim to reduce the ambiguities present in ordinary language.

Note that, in order to render his language as univocal as possible, Wilkins had even decided to eliminate from the tables names of mythological (therefore non-existent) beings such as Sirens, Griffins, Harpies and Phoenixes, which could be at most written in natural language as proper names of individuals (for an analogy with Russell’s preoccupations, see Frank 1979: 160).

Wilkins also admitted that his language was unsuited to capturing the minutiae of food and drink, like different types of grape, jam, coffee, tea and chocolate. The problem could naturally be solved, he claimed, through periphrasis; yet it is easy to foresee that to do so the language would have been overloaded with a lot of new, awkward syntagms, as happens today with papal encyclicals, where video-cassettes become sonorarum visualiumque taeniarum cistellulae, and advertising men turn into laudativis nuntiis vulgatores.

Besides, in Latin it would have been possible to avoid such monstrosities by coining new words such as videocapsulae or publicitarii (see Bettini 1992), while Wilkins‘ language seems to have closed the door to neologisms. The only way to escape this difficulty would be to assume that the list of primitives was open.”

“Figure 12.3 gives Wilkins‘ own illustration of the signs characterizing the 40 major genera as well as the signs used to indicate differences and species.

The fundamental sign is a simple dash with a modification at its center to indicate genus. Differences and species are indicated by little hooks and bars attached to the two extremities of the dash: those attached to the left extremity signify differences; those to the right signify species.

A different series of signs, extremely difficult to read, is provided to indicate opposition, grammatical forms, copula, adverbs, prepositions, conjunctions, etc., as we have already seen for analogous writing systems.

As I have said, the system also specifies the way in which the characters are to be pronounced. In figure 12.4 we see that each of the genera is assigned its own two-letter symbol, while the differences are expressed by the consonants B, D, G, P, T, C, Z, S, N and the species by the addition of seven vowels and two diphthongs. Here is one of Wilkins‘ own examples:

For instance if (De) signifie Element, then (Deb) must signifie the first difference; which (according to the Tables) is Fire: and (Debα) will denote the first Species, which is Flame. (Det) will be the fifth difference under that Genus, which is, Appearing meteor; (Detα) the first Species, viz. Rainbow; (Deta) the second, viz. Halo. (p. 415).

Figure 12.5 gives the first line of the Lord’s Prayer in characters.

The first sign indicates the first person plural of the possessive pronoun; the second is the sign of Economic Relations modified by a hook on the left, which indicates the first difference (relations of consanguinity), and another on the right which indicates the second species, Direct Ascendent.

The first two signs therefore mean “Our Father” and are pronounced Hai coba. As a matter of fact, the phonetic language is clearer also as a form of writing, and our following examples will mainly rely on it.”

“Already in Mercury, a book principally devoted to secret writing, published in 1641, Wilkins had begun to design a project for universal language. It was not until 1668, however, that he was ready to unveil his Essay towards a Real Character, and a Philosophical Language–the most complete project for a universal and artificial philosophical language that the seventeenth century was ever to produce.

Since “the variety of Letters is an appendix to the Curse of Babel” (p. 13), after a dutiful bow in the direction of the Hebrew language and a sketch of the evolution of languages from Babel onwards (including an examination of the Celto-Scythian hypothesis that we considered in ch. 5), and after an acknowledgment of his precursors and his collaborators in the compilation of classifications and of the final dictionary, Wilkins turned to his major task–the construction of a language founded on real characters “legible by any Nation in their own Tongue” (p. 13).

Wilkins observed that most earlier projects derived their list of characters from the dictionary of one particular language rather than drawing directly on the nature of things, and from that stock of notions held in common by all humanity.

Wilkins‘ approach required, as a preliminary step, a vast review of all knowledge to establish what these notions held in common by all rational beings really were.

Wilkins never considered that these fundamental notions might be Platonic ideas like Lull’s dignities. His list was rather based upon empirical criteria and he sought those notions to which all rational beings might either attest or, reasonably, be expected to attest: thus, if everybody agrees on the idea of a God, everybody would likewise agree on the botanical classification supplied to him by his colleague John Ray.

In reality, the image of the universe that Wilkins proposed was the one designed by the Oxonian culture of his time. Wilkins never seriously wondered whether other cultures might have organized the world after a different fashion, even though his universal language was designed for the whole of humanity.

The Tables and the Grammar

In appearance the classification procedure chosen by Wilkins was akin to the method of the Porphyrian Tree of Aristotelian tradition. Wilkins constructed a table of 40 major genera (see figure 12.1) subdivided into 251 characteristic differences.

From these he derived 2,030 species, which appear in pairs. Figure 12.2 provides a simplified example of the procedure: starting from the major genus of Beasts, after having divided them into viviparous and oviparous, and after having subdivided the viviparous ones into whole footed, cloven footed and clawed, Wilkins arrives at the species Dog / Wolf.

I might add parenthetically that Wilkins‘ tables occupy a full 270 pages of his ponderous folio, and hope that the reader will excuse the summary nature of the examples which follow.

After presenting the tables, which supposedly design the whole knowable universe, Wilkins turned his attention to his natural (or philosophical) grammar in order to establish morphemes and the markers for derived terms, which can permit the generation, from the primitives, of declensions, conjugations, suffixes and so on.

Such a simplified grammatical machinery should thus allow the speaker to articulate discourses, as well as to produce the periphrases through which terms from a natural language might be defined entirely through the primitives of the artificial one.

Having reached this stage, Wilkins was able to present his language of real characters. In fact, it splits into two different languages: (1) the first is an ideogrammatic form of writing, vaguely Chinese in aspect, destined to appear in print but never to be pronounced; (2) the second is expressed by alphabetic characters and is intended to be pronounced.

It is possible to speak properly of two separate languages because, even though the pronounceable characters were constructed according to the same compositional principle as the ideograms, and obey the same syntax, they are so different that they need to be learned apart.”

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George Dalgarno (1626-1687), Didascalocophus, or the Deaf and Dumb mans Tutor, Theater in Oxford, 1680. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“Figure 11.1 presents an extremely simplified, partial reconstruction of the tables, which limits itself to following only two of the subdivisions–animals with uncleft hooves and the principle passions.

The 17 fundamental genera are printed in bold capitals, and are marked with 17 capital letters. Intermediate genera and species are represented in lower case. Dalgarno also employs three “servile” letters: R signifies a reversal in meaning (if pon means love, pron means hate); V indicates that the letters that precede it are to be read as numbers; L signifies a medium between two extremes.

See for instance how from concrete, corporeal, physical entities, signified by an N, animals are deduced. See also how, in order to reach the subdivision animal, Dalgarno introduces an intermediate division (animal/inanimate) which is neither a genus nor a species, and is not marked by any letter.

The animals are subdivided into three classes–aquatic, aerial and terrestrial. Among the terrestrial animals (k) appear those with uncleft hooves [η], or perissodactyls. Thus the character Nηk stands for the class of perissodactyls. At this point, however, Dalgarno adds several sub-species–viz. the horse, elephant, mule and donkey.

As far as the accidents (E) are concerned, see for instance how the principal passions (o) are classified as species of the sensitive (P). After this, we are presented with a list that is not dichotomized: admiration takes pom as its character, because P is the fundamental genus and o is the intermediate genus. The m, however, is just the “number” that the species admiration is assigned in the list’s order.

It is curious that, for animals, the intermediate genus is given by the third letter in the character and the species by the second vowel, while for the accidents the opposite happens.

Dalgarno acknowledges the existence of such an irregularity, without offering any explanation (p. 52). The motive is doubtless euphony; still, there seems to have been nothing to prevent Dalgarno from assigning to the intermediate genera of concrete beings vowels instead of consonants and to the species consonants instead of vowels. In this way, he could have used the same criterion throughout the table.

The problem, however, is more complex than it seems. The expression Nηk applied to the perissodactyls is motived by the divisions; only an arbitrary decision, on the contrary, motivates the decision to specify elephant with the addition of an a.

But it is not the arbitrariness of the choice itself which creates problems; it is rather that while k means “those terrestrials which are animal because they are animated and therefore physically concrete” (so that the division explains or reflects in some way the nature of the thing itself), the a at the end of Nηka (sic) only means “that thing which is numbered a on the list of perissodactyls and is called elephant.”

The same observation applies to the m in pom. All it really signifies is “position number m on the list of those sensitive accidents which are principal passions, i.e. admiration.” Since the dichotomic division does not reach the lower species, Dalgarno is forced to tack on lists in an alphabetical or almost alphabetical order.

Dalgarno (p. 42) noted, however, that this procedure was simply a mnemonic artifice for those who did not wish to learn the defining name. At the end of the book there is indeed a philosophical lexicon giving the characters for many terms in Latin.

In particular, there exists at the end of this list a special section devoted to concrete physical objects. Thus is seems that a philosophical definition of final species is possible; the only difficulty is that, given the purely exemplary nature of the lexicon, Dalgarno has left the naming of a large number of species up to the speaker, who can infer it from the tables.

But even in this instance, “the tables only classify and name up to a point; the lexicon provides the rest of the definition but not the classification” (Slaughter 1982: 152).

Dalgarno may not have considered it indispensable to arrive at a classification of complex entities in all their particularities, yet making definitions requires classification. As a result the decision on how to classify complex entities, and, consequently, what name to give them, seems left as it were to the discretion of the user of the language.

Thus, ironically, a system that was intended to provide a single set of objective and univocal definitions ends up by lending itself to the creative fancies of its users. Here are some of Dalgarno’s own suggestions (I have separated the radicals with a slash to make them more decipherable):

horse = Nηk/pot = animal with uncleft hoof/courageous [why could we not say the same of the elephant?]

Dalgarno also admitted that the same object regarded from a different perspective might take different names. The elephant can be called Nηksyf (uncleft hoof / superlative) or Nηkbeisap (uncleft hoof / mathematical accident / architectural metaphor for the proboscis).

It is not a system that is at all easy to memorize. The difference between Nηke, donkey, and Nηko, mule, is minimal and easy to muddle. Dalgarno advised the reader to use old mnemonic tricks.

The name for table was fran; the name for plough was flan; Dalgarno suggested associating the first with FRANce and the second with FLANders. In this way the speaker needed to learn both a philosophical language and a mnemonic code.

Dalgarno somewhat compensates the reader for the transcendental difficulties in the lexicon and the rules of composition by providing a grammar and syntax of great simplicity.

All that remains of the categories of classical grammar is the noun along with several pronouns (I = lal, you = lêl, he = lel . . . ). Adverbs, adjectives, comparatives and even verbal forms are derived by adding suffixes to nouns.

The notion that verbs could all be reduced to the copula plus an adjective already circulated among the Modists in the thirteenth century; it was taken up by Campanella in the Philosophia rationalis(1638) and accepted by both Wilkins and Leibniz.

Dalgarno’s treatment of syntax was no less radical (see Pellerey 1992c). Although other projects for philosophic languages preserved the Latin model, Dalgarno eliminated the declensions for nouns.

All that counted was word order: the subject preceded the verb and the verb preceded the object. The ablative absolute was rendered by temporal particles which stood for terms like cum, post or dum.

The genitive was rendered either by an adjectival suffix or by a formula of possession (shf = to belong). Shumaker has commented (1982: 155) that forms of the latter type are adopted by pidgin English, in which the phrase “master’s hand” is rendered “hand-belong-master.”

Simplified to this degree, the language seems syntactically crude. Yet Dalgarno, deeply suspicious of rhetorical embellishments, was convinced that only an essential logical structure gave a language an austere elegance.

Besides, grace, elegance and transparent clarity were given full play in the composition of the names, and for this reason, Dalgarno compared his language to the philosophical language par excellence, ancient Greek.

One final aspect of Dalgarno’s system that he shared with both Wilkins and Lodwick has been underlined by Frank (1979: 65ff). By using particles, prefixed and suffixed to names, to transform nouns into other grammatical categories, changing their meanings thereby, and inserting prepositions, such as per, trans, praeter, supra, in and a, among the mathematical accidents–and thus as equivalent to nouns–Dalgarno tended “to postulate an all-comprehending semantics which took over all, or almost all of the functions traditionally assigned to grammar.”

Dalgarno, in other words, abolished the classical distinction between categorematic terms, or terms that have independent meanings, and syncategorematic terms, or terms which acquire a meaning only within a context.

This, in logic, is equivalent to the distinction between logical variables that can be bound to specific meanings and logical connectives. This is a tendency that is contrary to the tenets of modern logic; yet it is consistent with some trends in contemporary semantics.”

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George Dalgarno (1626-1687), title page of Ars Signorum, printed by J. Hayes, London, 1661. Published 20 years before Didascalocophus, Ars signorumpreceded Bishop Wilkin‘s speculations on a “real character and a philosophical language.” This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“It is difficult to make a precise evaluation of George Dalgarno’sArs signorum, published in 1661. In contrast to Wilkin’s Essay, Dalgarno’s tables are summary and the text, in its expository sections, is written in a language that is extremely cryptic, sometimes contradictory, and almost always strikingly allusive.

The book is filled with printer’s errors, especially where Dalgarno provides examples of real characters–not an inconsiderable problem in reading a language where the misprint of one letter changes the whole sense of the character.

We might note that the difficulty in printing a text free of errors shows how cumbersome the philosophic languages were, even for their own creators.

Dalgarno was a Scottish schoolmaster who passed most of his life at Oxford, where he taught grammar at a private school. He was in touch with all the contemporary scholars at the university, and in the list of acknowledgements at the beginning of his book he mentions men such as Ward, Lodwick, Boyle and even Wilkins.

It is certain that, as he was preparing his Essay (published seven years later), Wilkins contacted Dalgarno and showed him his own tables. Dalgarno regarded them as too detailed, and chose to follow what seemed to him an easier path.

When Wilkins finally made his project public, however, Dalgarno felt himself to be the victim of plagiarism. The suspicion was unjust: Wilkins had accomplished what Dalgarno had only promised to do.

Besides, various other authors had already anticipated many of the elements appearing in the project of Dalgarno. Still, Wilkins resented the insinuation of wrong-doing. In the acknowledgements that prefaced his Essay, Wilkins was prodigal with his thanks to inspirers and collaborators alike, but the name of Dalgarno does not appear–except in an oblique reference to “another person.” (b2r).

Although we are not informed of the conclusions that they finally reached, subsequent tradition, from Locke to the Encyclopédie, invariably treated Wilkins as the author of the most important project.

Perhaps the only scholar who considered Dalgarno respectfully was Leibniz, who, in a rough draft for his own encyclopedia, reproduced Dalgarno’s list of entities almost literally (see Rossi 1960: 272).

Wilkins, of course, was perfectly at home at the Royal Society. He served as its secretary, and could freely avail himself of the help, advice, patronage and attention of his fellow members. Dalgarno, by contrast, was not even a member of the university.

Dalgarno saw that a universal language needed to comprehend two distinct aspects: first, a content-plane, that is, a classification of all knowledge, and that was a task for a philosopher; second, an expression-level, that is, a grammar that organized the characters so that they can properly denote the content elements–and this was a task for a grammarian.

Dalgarno regarded himself as a grammarian rather than a philosopher; hence he merely outlined the principles of classification upon which his language would be based, hoping that others might carry this task to fruition.

As a grammarian, Dalgarno was sensitive to the problem that his language would need to be spoken and not just written. He was aware of the reserves Descartes had expressed about the difficulty of devising a philosophic language that might be pronounced by speakers of differing tongues; thus he introduced his project with a phonetic analysis which sought to identify those sounds which were most easily compatible with the human organs of speech.

The letters from which he later composed his character were not, as they might seem, chosen arbitrarily; he chose instead those which he considered most easy to utter. Even when he came to elaborate the syntagmatic order of his character, he remained concerned with ease of pronunciation.

To this end, he made sure that consonants were always followed by vowels, inserting in his character a number of diphthongs whose function is purely euphonious. This concern certainly ensured ease of pronunciation; unfortunately, it also rendered his character increasingly difficult to identify.

After phonetics, Dalgarno passed to the problem, of the semantic primitives. He believed that these could all be derived solely in terms of genus, species and difference, arguing that such a system of embedded dichotomies was the easiest to remember (p. 29).

For a series of logico-philosophical reasons (explained pp. 30ff), he excluded negative differences from his system, retaining only those which were positive.

The most ambitious feature of Dalgarno’s project (and Wilkin’s as well) was that his classification was to include not only natural genera and species (comprehending the most precise variations in animals and plants) but also artifacts and accidents–a task never attempted by the Aristotelian tradition (see Shumaker 1982: 149).

In fact, Dalgarno based his system of classification on the rather bold assumption that all individual substances could be reduced to an aggregate of accidents (p. 44). This is an assumption which, as I have tried to show elsewhere (Eco 1984: 2.4.3), arises as an almost mechanical consequence of using Porphyry’s Tree as a basis for classification; it is a consequence, moreover, that the entire Aristotelian tradition has desperately tried to ignore.

Dalgarno confronted the problem, even though recognizing that the number of accidents was probably infinite. He was also aware that the number of species at the lowest order was unmanageably large–he calculated that they would number between 4,000 and 10,000.

This is probably one of the reasons why he rejected the help of Wilkins, who was to persevere until he had classified 2,030 species. Dalgarno feared that such a detailed classification ran the risk of a surgeon who, having dissected his cadavers into minute pieces, could no longer tell which piece belonged to Peter and which to John (p. 33).

In his endeavor to contain the number of primitives, Dalgarno decided to introduce tables in which he took into consideration only fundamental genera (which he numbered at 17), together with the intermediary genera and the species.

Yet, in order to gather up all the species in this tripartite division, Dalgarno was forced to introduce into his tables a number of intermediate disjunctions. These even received names in the language: warm-blooded animals, for example, are called NeiPTeik; quadrupeds are named Neik.

Yet in the names only the letters for genera, intermediary genera, and species are taken into account. (Mathematical entities are considered as concrete bodies on the assumption that entities like points and lines are really forms).”

“Nevertheless, such a dictionary-like structure would not allow us to define the difference between a cat and a tiger, or even between a canine and a feline animal. To do this, it is necessary to insert differences into the classification.

Aristotle, in his studies of definition, said that, in order to define the essence of a thing, we should select such attributes which “although each of them has a wider extension than the subject, all together they have not” (Posterior Analytics II, 96a, 35).

Such a structured representation was known in the Middle Ages as Porphyry’s Tree (because it was derived from the Isagoge of the Neo-Platonic philosopher Porphyry, living in the second-third century AD), and was still taken as a definitional model by the English searchers for a real character.

In a Porphyrian Tree each genus is divided by two differences which constitute a pair of opposites. Each genus, with the addition of one of its divisive differences, produces an underlying species, which is so defined by its genus and its constitutive difference.

In figure 10.2, there is an example of how a Porphyrian Tree establishes the difference between human beings and gods (understood as natural forces) and between human beings and beasts.

The terms in upper-case refer to genera and species while those in lower-case refer to differences, that is, to particular accidents which occur only in a given species. We see that the diagram defines a human being as a “rational and mortal animal,” which, in classical terms, is considered a satisfactory definition because there cannot be a rational and mortal animal which is not a human being, and only human beings are so.

Unfortunately this diagram does not tell us anything about the differences between dogs and cats, or horses and wolves, or cats and tigers. In order to obtain new definitions, new differences need to be inserted into the diagram.

Besides this, we can see that, although differences occur in one species, in this tree there are differences, such as “mortal/immortal,” which occur in two different species.

This makes it difficult to know whether or not the same differences will be reproduced at some further point in the tree when it becomes necessary to specify the difference not just between dogs and cats, but also between violets and roses, diamonds and sapphires, and angels and demons.

Even taxonomy as practiced by modern zoology defines through dichotomies. Dogs are distinguished from wolves, and cats from tigers, on the basis of a dichotomy by taxonomic entities known as taxa (figure 10.3).

Yet modern zoologists are well aware that a system of classification is not the same as a system of definitions.

Classification does not capture the essence of the thing itself; it simply embeds things in a system of increasingly inclusive classes, where the lower nodes are linked by entailment to the upper ones: if something is a Canis familiaris, it cannot but be, by entailment, a Canis, a canid and a fissiped.

But Canidae and Fissipeda are taken as primitives only in the framework of the classification and are not considered as semantic primitives.

Zoologists know that, within their classification, at the node Canidae they must presuppose a set of properties common to the whole family, and that at the node Carnivora there is a set of properties common to the whole order: in the same vein, “mammal” is not a semantic primitive but a technical name which stands for (more or less) “viviparous animal which nourishes its young by the secretion of milk through its mammary glands.”

The name of a substance can be either designative (thus indicating the genus to which that substance belongs) or diagnostic, that is, transparent and self-definatory.

In Speciesplantarumby Linnaeus (1753), given the two species, Arundo calamogrostis and Arundo arenaria, their designative names show that they belong to the same genus and establish their difference; however, their properties are then made clearer by a diagnostic description which specifies that the Arundo calamogrostis is “calycibus unifloris, cumulo ramoso,” while the Arundo arenaria is “calycibus unifloris, foliis involutiis, mucronato pungentibus” (see Slaughter 1982: 80).

However, the terms used for this description are no longer pseudo-primitives–like those of the metalanguage of taxas; they are terms of the common natural language used for diagnostic purposes.

By contrast, for the authors of a priori languages, each expression had to express all the properties of the designated thing. We shall see how such a difficulty will affect all the projects discussed in the following chapters.”

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William Blake (1757-1827), The Tyger, 1794. Scan of a plate printed by the author collected in Songs of Experience, designed after 1789 and printed in 1794. Copies A and B are both held by the British Museum. This work is in the public domain in its country or origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“In order to design characters that directly denote notions (if not the things themselves that these notions reflect), two conditions must be fulfilled: (1) the identification of primitive notions; (2) the organization of these primitives into a system which represents the model of the organization of content.

It is for this reason that these languages qualify as philosophical and a priori. Their formulation required individuating and organizing a sort of philosophical “grammar of ideas” that was independent from any natural language, and would therefore need to be postulated a priori.

Only when the content-plane had been organized would it be possible to design the characters that would express the semantic primitives. As Dalgarno was later to put it, the work of the philosopher had to precede that of the linguist.

For the polygraphers, invention was simply the job of assigning numbers to a collection of words from a given natural language. The inventors of philosophic a priori languages needed to invent characters that referred to things or notions: this meant that their first step was to draw up a list of notions and things.

This was not an easy task. Since the lexicon of any natural language is always finite in number, while the number of things, including physically existing objects, rational entities, accidents of all types, is potentially infinite, in order to outline a list of real characters it is necessary to design an inventory which is not only universal: it must also be in some way limited.

It is mandatory to establish which notions are the most universally common, and then to go on by analyzing the derivative notions according to a principle of compositionality by primitive features.

In this way, the entire set of possible contents that the language is able to express has to be articulated as a set of “molecular aggregates” that can be reduced to atomic features.

Suppose we had three semantic atoms such as ANIMAL, CANINE and FELINE. Using them, we might analyze the following four expressions:

Umberto Eco, The Search for the Perfect Language, p. 222.

Yet the features that analyze the content of the above expressions ought to be entities totally extraneous to the object language.

The semantic feature CANINE, for example, must not be identifiable with the word canine. The semantic features ought to be extra-linguistic and possibly innate entities. At least they should be postulated as such, as when one provides a computer with a dictionary in which every term of a given language can be split into minor features posited by the program.

In any case, the initial problem is how to identify these primitive and atomic features and set a limit on their number.

If one means by “primitive” a simple concept, it is very difficult to decide whether and when one concept is simpler than another. For the normal speaker, the concept of “man” is simpler–that is, easier to understand–than the one of “mammal.”

By contrast, according to every sort of semantic analysis, “mammal” is a component of (therefore simpler than) “man.” It has been remarked that for a common dictionary it is easier to define terms like infarct than terms like to do (Rey-Debone 1971: 194ff).

We might decide that the primitives depend on our world experience; they would correspond to those that Russell (1940) called “object-words,” whose meanings we learn by ostension, in the same way as a child learns the meaning of the word red by finding it associated with different occurrences of the same chromatic experience.

By contrast, according to Russell, there are “dictionary-words” that can be defined through other words, such as pentagram. Yet Russell remarks, for a child who had grown up in a room decorated with motifs in the form of a pentagram, this word would be an object one.

Another alternative would be to regard primitives as innate Platonic ideas. This solution would be philosophically impeccable; yet not even Plato himself was able to establish what and how many these innate ideas were.

Either there is an idea for every natural kind (for horses, platypuses, fleas, elms and so on–which means an atomic feature for every element of the furnishing of the world), or there are a few abstract ideas (the One, the Many, the Good and mathematical concepts), but through them it would be difficult to define compositionally a horse or a platypus.

Suppose instead we decided to order the system of primitives by dichotomic disjunctions so that, by virtue of the systematic relations obtaining between the terms, they must remain finite in number.

With such a structure we would be able to define by a finite number of atomic primitives a great number of molecular entities. A good example of this alternative is the reciprocally embedded system of hyponyms and hyperonyms used by lexicographers.

It is organized hierarchically in the form of a tree of binary disjunctions: to each opposed pair of hyponyms there corresponds a single hyperonym, which, in its turn, is opposed to another hyperonym to form the next level of hyponyms, to which a further hyperonym will correspond, and so on.

In the end, regardless of how many terms are embedded in the system, the whole structure must finish at its apex in a single patriarch-hyperonym.

Thus the example of the table on p. 222 above would take the following format:

According to many contemporary authors, this kind of semantic structure would analyze the content in the format of a dictionary (as opposed to an encyclopedia).

In an encyclopedia-like representation one introduces elements of world knowledge (for example that a tiger is a yellow cat with stripes on its fur), and these elements are potentially infinite in number.

In a dictionary-like representation the features are, on the contrary, analytic, in the sense that they are the only and necessary conditions for the definition of a given content: a cat is necessarily a feline and an animal and it would be contradictory to assert that a cat is not an animal, since the feature “animal” is analytically a part of the definition of cat.

In this sense it would be easy to distinguish analytical from synthetical judgments. “A tiger is a feline animal” would be analytical, so uniquely depending on our rigorously organized dictionary competence (which is exclusively linguistic), while “tigers are man-eaters” would depend on our extra-linguistical world knowledge.”